arXiv subjects

Wen Yuan

Publications and source records attributed to Wen Yuan.

At least 91 records · Page 5Linked to original sources

arXiv2021

Functional Calculus on BMO-type Spaces of Bourgain, Brezis and Mironescu

A nonlinear superposition operator $T_g$ related to a Borel measurable function $g:\ {\mathbb C}\to {\mathbb C}$ is defined via $T_g(f):=g\circ f$ for any complex-valued function $f$ on ${\mathbb R^n}$. This article is devoted to investigating the mapping properties of $T_g$ on a new BMO type space recently introduced by Bourgain, Brezis and Mironescu [J. Eur. Math. Soc. (JEMS) 17 (2015), 2083-2101], as well as its VMO and CMO type subspaces. Some sufficient and necessary conditions for the inclusion result and the continuity property of $T_g$ on these spaces are obtained.

math.CA↗

arXiv2021

Compactness Characterizations of Commutators on Ball Banach Function Spaces

Let $X$ be a ball Banach function space on ${\mathbb R}^n$. Let $Ω$ be a Lipschitz function on the unit sphere of ${\mathbb R}^n$,which is homogeneous of degree zero and has mean value zero, and let $T_Ω$ be the convolutional singular integral operator with kernel $Ω(\cdot)/|\cdot|^n$. In this article, under the assumption that the Hardy--Littlewood maximal operator $\mathcal{M}$ is bounded on both $X$ and its associated space, the authors prove that the commutator $[b,T_Ω]$ is compact on $X$ if and only if $b\in{\rm CMO}({\mathbb R}^n)$. To achieve this, the authors mainly employ three key tools: some elaborate estimates, given in this article, on the norm in $X$ of the commutators and the characteristic functions of some measurable subset,which are implied by the assumed boundedness of ${\mathcal M}$ on $X$ and its associated space as well as the geometry of $\mathbb R^n$; the complete John--Nirenberg inequality in $X$ obtained by Y. Sawano et al.; the generalized Fréchet--Kolmogorov theorem on $X$ also established in this article. All these results have a wide range of applications. Particularly, even when $X:=L^{p(\cdot)}({\mathbb R}^n)$ (the variable Lebesgue space), $X:=L^{\vec{p}}({\mathbb R}^n)$ (the mixed-norm Lebesgue space), $X:=L^Φ({\mathbb R}^n)$ (the Orlicz space), and $X:=(E_Φ^q)_t({\mathbb R}^n)$ (the Orlicz-slice space or the generalized amalgam space), all these results are new.

math.FA↗

arXiv2020

XMO and Weighted Compact Bilinear Commutators

To study the compactness of bilinear commutators of certain bilinear Calderón--Zygmund operators which include (inhomogeneous) Coifman--Meyer bilinear Fourier multipliers and bilinear pseudodifferential operators as special examples, Torres and Xue [Rev. Mat. Iberoam. 36 (2020), 939--956] introduced a new subspace of BMO$\,(\mathbb{R}^n)$, denoted by XMO$\,(\mathbb{R}^n)$, and conjectured that it is just the space VMO$\,(\mathbb{R}^n)$ introduced by D. Sarason. In this article, the authors give a negative answer to this conjecture by establishing an equivalent characterization of XMO$\,(\mathbb{R}^n)$, which further clarifies that XMO$\,(\mathbb{R}^n)$ is a proper subspace of VMO$\,(\mathbb{R}^n)$. This equivalent characterization of XMO$\,(\mathbb{R}^n)$ is formally similar to the corresponding one of CMO$\,(\mathbb{R}^n)$ obtained by A. Uchiyama, but its proof needs some essential new techniques on dyadic cubes as well as some exquisite geometrical observations. As an application, the authors also obtain a weighted compactness result on such bilinear commutators, which optimizes the corresponding result in the unweighted setting.

math.CA↗

arXiv2020

Bilinear Decomposition and Divergence-Curl Estimates on Products Related to Local Hardy Spaces and Their Dual Spaces

Let $p\in(0,1)$, $α:=1/p-1$ and, for any $τ\in [0,\infty)$, $Φ_{p}(τ):=τ/(1+τ^{1-p})$. Let $H^p(\mathbb R^n)$, $h^p(\mathbb R^n)$ and $Λ_{nα}(\mathbb{R}^n)$ be, respectively, the Hardy space, the local Hardy space and the inhomogeneous Lipschitz space on $\mathbb{R}^n$. In this article, applying the inhomogeneous renormalization of wavelets, the authors establish a bilinear decomposition for multiplications of elements in $h^p(\mathbb R^n)$ [or $H^p(\mathbb R^n)$] and $Λ_{nα}(\mathbb{R}^n)$, and prove that these bilinear decompositions are sharp in some sense. As applications, the authors also obtain some estimates of the product of elements in the local Hardy space $h^p(\mathbb R^n)$ with $p\in(0,1]$ and its dual space, respectively, with zero $\lfloor nα\rfloor$-inhomogeneous curl and zero divergence, where $\lfloor nα\rfloor$ denotes the largest integer not greater than $nα$. Moreover, the authors find new structures of $h^{Φ_p}(\mathbb R^n)$ and $H^{Φ_p}(\mathbb R^n)$ by showing that $h^{Φ_p}(\mathbb R^n)=h^1(\mathbb R^n)+h^p(\mathbb R^n)$ and $H^{Φ_p}(\mathbb R^n)=H^1(\mathbb R^n)+H^p(\mathbb R^n)$ with equivalent quasi-norms, and also prove that the dual spaces of both $h^{Φ_p}(\mathbb R^n)$ and $h^p(\mathbb R^n)$ coincide. These results give a complete picture on the multiplication between the local Hardy space and its dual space.

math.CA↗

arXiv2020

Real-Variable Characterizations of Local Orlicz-Slice Hardy Spaces with Application to Bilinear Decompositions

Recently, both the bilinear decompositions $h^1(\mathbb{R}^n)\times \mathrm{\,bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n)+h_\ast^Φ(\mathbb{R}^n)$ and $h^1(\mathbb{R}^n) \times \mathrm{bmo}(\mathbb{R}^n) \subset L^1 (\mathbb{R}^n) + h^{\log}(\mathbb{R}^n)$ were established. In this article, the authors prove in some sense that the former is sharp, while the latter is not. To this end, the authors first introduce the local Orlicz-slice Hardy space which contains the variant $h_\ast^Φ(\mathbb{R}^n)$ of the local Orlicz Hardy space introduced by A. Bonami and J. Feuto as a special case, and obtain its dual space by establishing its characterizations via atoms, finite atoms and various maximal functions, which are new even for $h_\ast^Φ(\mathbb R^n)$. The relationships $h_\ast^Φ(\mathbb{R}^n) \subsetneqq h^{\log}(\mathbb{R}^n)$ is also clarified.

math.CA↗

arXiv2020

Detecting Suspected Epidemic Cases Using Trajectory Big Data

Emerging infectious diseases are existential threats to human health and global stability. The recent outbreaks of the novel coronavirus COVID-19 have rapidly formed a global pandemic, causing hundreds of thousands of infections and huge economic loss. The WHO declares that more precise measures to track, detect and isolate infected people are among the most effective means to quickly contain the outbreak. Based on trajectory provided by the big data and the mean field theory, we establish an aggregated risk mean field that contains information of all risk-spreading particles by proposing a spatio-temporal model named HiRES risk map. It has dynamic fine spatial resolution and high computation efficiency enabling fast update. We then propose an objective individual epidemic risk scoring model named HiRES-p based on HiRES risk maps, and use it to develop statistical inference and machine learning methods for detecting suspected epidemic-infected individuals. We conduct numerical experiments by applying the proposed methods to study the early outbreak of COVID-19 in China. Results show that the HiRES risk map has strong ability in capturing global trend and local variability of the epidemic risk, thus can be applied to monitor epidemic risk at country, province, city and community levels, as well as at specific high-risk locations such as hospital and station. HiRES-p score seems to be an effective measurement of personal epidemic risk. The accuracy of both detecting methods are above 90\% when the population infection rate is under 20\%, which indicates great application potential in epidemic risk prevention and control practice.

stat.AP↗

arXiv2020

Weighted Global Regularity Estimates for Elliptic Problems with Robin Boundary Conditions in Lipschitz Domains

Let $n\ge2$ and $Ω$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations of divergence form with real-valued, bounded, measurable coefficients in $Ω$. More precisely, let $p\in(n/(n-1),\infty)$. Using a real-variable argument, the authors obtain two necessary and sufficient conditions for $W^{1,p}$ estimates of solutions to Robin boundary value problems, respectively, in terms of a weak reverse Hölder inequality with exponent $p$ or weighted $W^{1,q}$ estimates of solutions with $q\in(n/(n-1),p]$ and some Muckenhoupt weights. As applications, the authors establish some global regularity estimates for solutions to Robin boundary value problems of second order elliptic equations of divergence form with small $\mathrm{BMO}$ coefficients, respectively, on bounded Lipschitz domains, $C^1$ domains or (semi-)convex domains, in the scale of weighted Lebesgue spaces, via some quite subtle approach which is different from the existing ones and, even when $n=3$ in case of bounded $C^1$ domains, also gives an alternative correct proof of some know result. By this and some technique from harmonic analysis, the authors further obtain the global regularity estimates, respectively, in Morrey spaces, (Musielak--)Orlicz spaces and variable Lebesgue spaces

math.AP↗

arXiv2020

Multiphase interpolating digital power amplifiers for TX beamforming

This paper presents a 4-channel beamforming TX implemented in 65nm CMOS. Each beamforming TX is comprised of a C-2C split-array multiphase switched-capacitor power amplifier (SAMP-SCPA). This is the first use of multiphase interpolation (MPI) for beam-steering. This technique is ideal for low-frequency beamforming and MIMO, as it does not require passive or LO based phase shifters. The SCPA is ideal to use as the core element since it can perform frequency translation, data conversion and drive an output at high power and efficiency in a compact die area. A prototype 4-element beamforming TX, occupying 2 mm X 2.5 mm, can achieve peak output power of 24.4 dBm with a peak system efficiency (SE) of 24%, while achieving < 1° phase resolution and <1 dB gain error. When transmitting a 15 MHz, 64 QAM long-term evolution (LTE) signal it outputs 18.4 dBm at 14% SE with a measured adjacent channel leakage ratio (ACLR) < -30 dBc and error vector magnitude (EVM) of 3.27 %-rms at 1.75 GHz. A synthesized beam pattern based on measured results from a single die achieves <0.32°-rms beam angle error and <0.15 dB rms beam amplitude error.

eess.SP↗

arXiv2019

Real-Variable Characterizations of New Anisotropic Mixed-Norm Hardy Spaces

Let $\vec{p}\in(0,\infty)^n$ and $A$ be a general expansive matrix on $\mathbb{R}^n$. In this article, via the non-tangential grand maximal function, the authors first introduce the anisotropic mixed-norm Hardy spaces $H_A^{\vec{p}}(\mathbb{R}^n)$ associated with $A$ and then establish their radial or non-tangential maximal function characterizations. Moreover, the authors characterize $H_A^{\vec{p}}(\mathbb{R}^n)$, respectively, by means of atoms, finite atoms, Lusin area functions, Littlewood-Paley $g$-functions or $g_λ^\ast$-functions via first establishing an anisotropic Fefferman-Stein vector-valued inequality on the mixed-norm Lebesgue space $L^{\vec{p}}(\mathbb{R}^n)$. In addition, the authors also obtain the duality between $H_A^{\vec{p}}(\mathbb{R}^n)$ and the anisotropic mixed-norm Campanato spaces. As applications, the authors establish a criterion on the boundedness of sublinear operators from $H_A^{\vec{p}}(\mathbb{R}^n)$ into a quasi-Banach space. Applying this criterion, the authors then obtain the boundedness of anisotropic convolutional $δ$-type and non-convolutional $β$-order Calderón-Zygmund operators from $H_A^{\vec{p}}(\mathbb{R}^n)$ to itself [or to $L^{\vec{p}}(\mathbb{R}^n)$]. As a corollary, the boundedness of anisotropic convolutional $δ$-type Calderón-Zygmund operators on the mixed-norm Lebesgue space $L^{\vec{p}}(\mathbb{R}^n)$ with $\vec{p}\in(1,\infty)^n$ is also presented.

math.CA↗

arXiv2019

Real-Variable Characterizations of Local Hardy Spaces on Spaces of Homogeneous Type

Suppose that $(X,d,μ)$ is a space of homogeneous type, with upper dimension $μ$, in the sense of R. R. Coifman and G. Weiss. Let $η$ be the Hölder regularity index of wavelets constructed by P. Auscher and T. Hytönen. In this article, the authors introduce the local Hardy space $h^{*,p}(X)$ via local grand maximal functions and also characterize $h^{*,p}(X)$ via local radial maximal functions, local non-tangential maximal functions, locally atoms and local Littlewood--Paley functions. Furthermore, the authors establish the relationship between the global and the local Hardy spaces. Finally, the authors also obtain the finite atomic characterizations of $h^{*,p}(X)$. As an application, the authors give the dual spaces of $h^{*,p}(X)$ when $p\in(ω/(ω+η),1)$, which further completes the result of G. Dafni and H. Yue on the dual space of $h^{*,1}(X)$. This article also answers the question of R. R. Coifman and G. Weiss on the nonnecessity of any additional geometric assumptions except the doubling condition for the radial maximal function characterization of $H^1_{\mathrm{cw}}(X)$ when $μ(X)<\infty$.

math.CA↗

arXiv2019

The Haar System in Besov-type Spaces

Some Besov-type spaces $B^{s,τ}_{p,q}(\mathbb{R}^n)$ can be characterized in terms of the behavior of the Fourier--Haar coefficients. In this article, the authors discuss some necessary restrictions for the parameters $s$, $τ$, $p$, $q$ and $n$ of this characterization. Therefore, the authors measure the regularity of the characteristic function $\mathcal X$ of the unit cube in $\mathbb{R}^n$ via the Besov-type spaces $B^{s,τ}_{p,q}(\mathbb{R}^n)$. Furthermore, the authors study necessary and sufficient conditions such that the operation $\langle f, \mathcal{X} \rangle$ generates a continuous linear functional on $B^{s,τ}_{p,q}(\mathbb{R}^n)$.

math.CA↗

arXiv2019

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces I: Decompositions with Applications to Boundedness of Calderón--Zygmund Operators

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, the authors introduce the weak Hardy-type space $WH_X({\mathbb R}^n)$, associated with $X$, via the radial maximal function. Assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on $X$ as well as it is bounded on both the weak ball quasi-Banach function space $WX$ and the associated space, the authors then establish several real-variable characterizations of $WH_X({\mathbb R}^n)$, respectively, in terms of various maximal functions, atoms and molecules. As an application, the authors obtain the boundedness of Calderón--Zygmund operators from the Hardy space $H_X({\mathbb R}^n)$ to $WH_X({\mathbb R}^n)$, which includes the critical case. All these results are of wide applications. Particularly, when $X:=M_q^p({\mathbb R}^n)$ (the Morrey space), $X:=L^{\vec{p}}({\mathbb R}^n)$ (the mixed-norm Lebesgue space) and $X:=(E_Φ^q)_t({\mathbb R}^n)$ (the Orlicz-slice space), which are all ball quasi-Banach function spaces but not quasi-Banach function spaces, all these results are even new. Due to the generality, more applications of these results are predictable.

math.CA↗

arXiv2019

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood--Paley Characterizations and Real Interpolation

Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on $X$ as well as it is bounded on both the weak ball quasi-Banach function space $WX$ and the associated space, the authors establish various Littlewood--Paley function characterizations of $WH_X({\mathbb R}^n)$ under some weak assumptions on the Littlewood--Paley functions. The authors also prove that the real interpolation intermediate space $(H_{X}({\mathbb R}^n),L^\infty({\mathbb R}^n))_{θ,\infty}$, between the Hardy space associated with $X$, $H_{X}({\mathbb R}^n)$, and the Lebesgue space $L^\infty({\mathbb R}^n)$, is $WH_{X^{{1}/{(1-θ)}}}({\mathbb R}^n)$, where $θ\in (0, 1)$. All these results are of wide applications. Particularly, when $X:=M_q^p({\mathbb R}^n)$ (the Morrey space), $X:=L^{\vec{p}}({\mathbb R}^n)$ (the mixed-norm Lebesgue space) and $X:=(E_Φ^q)_t({\mathbb R}^n)$ (the Orlicz-slice space), all these results are even new; when $X:=L_ω^Φ({\mathbb R}^n)$ (the weighted Orlicz space), the result on the real interpolation is new and, when $X:=L^{p(\cdot)}({\mathbb R}^n)$ (the variable Lebesgue space) and $X:=L_ω^Φ({\mathbb R}^n)$, the Littlewood--Paley function characterizations of $WH_X({\mathbb R}^n)$ obtained in this article improves the existing results via weakening the assumptions on the Littlewood--Paley functions.

math.CA↗

arXiv2019

John--Nirenberg--Campanato Spaces

Let $p\in (1,\infty)$, $q\in[1,\infty)$, $α\in [0,\infty)$ and $s$ be a non-negative integer. In this article, the authors introduce the John--Nirenberg-Campanato space $JN_{(p,q,s)_α}(\mathcal{X})$, where $\mathcal{X}$ is ${\mathbb R}^n$ or any closed cube $Q_0\subsetneqq{\mathbb R}^n$, which when $α=0$ and $s=0$ coincides with the $JN_p$-space introduced by F. John and L. Nirenberg in the sense of equivalent norms. The authors then give the predual space of $JN_{(p,q,s)_α}(\mathcal{X})$ and a John-Nirenberg type inequality of John--Nirenberg-Campanato spaces. Moreover, the authors prove that the classical Campanato space serves as a limit space of $JN_{(p,q,s)_α}(\mathcal{X})$ when $p\to \infty$.

math.CA↗

arXiv2018

New Characterizations of Musielak-Orlicz-Sobolev Spaces via Sharp Ball Averaging Functions

In this article, the authors establish a new characterization of the Musielak--Orlicz--Sobolev space on $\mathbb{R}^n$, which includes the classical Orlicz--Sobolev space, the weighted Sobolev space and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. Hästö and A. M. Ribeiro [Commun. Contemp. Math. 19 (2017), 1650022, 13 pp] via weakening the assumption $f\in L^1(\mathbb R^n)$ into $f\in L_{\mathrm{loc}}^1(\mathbb R^n)$, which was conjectured to be true by Hästö and Ribeiro in the aforementioned same article.

math.CA↗

arXiv2018

Dual Spaces of Anisotropic Mixed-Norm Hardy Spaces

Let $\vec{a}:=(a_1,\ldots,a_n)\in[1,\infty)^n$, $\vec{p}:=(p_1,\ldots,p_n)\in(0,\infty)^n$ and $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ be the anisotropic mixed-norm Hardy space associated with $\vec{a}$ defined via the non-tangential grand maximal function. In this article, the authors give the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, which was asked by Cleanthous et al. in [J. Geom. Anal. 27 (2017), 2758-2787]. More precisely, via first introducing the anisotropic mixed-norm Campanato space $\mathcal{L}_{\vec{p},\,q,\,s}^{\vec{a}}(\mathbb{R}^n)$ with $q\in[1,\infty]$ and $s\in\mathbb{Z}_+:=\{0,1,\ldots\}$, and applying the known atomic and finite atomic characterizations of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$, the authors prove that the dual space of $H_{\vec{a}}^{\vec{p}}(\mathbb{R}^n)$ is the space $\mathcal{L}_{\vec{p},\,r',\,s}^{\vec{a}}(\mathbb{R}^n)$ with $\vec{p}\in(0,1]^n$, $r\in(1,\infty]$, $1/r+1/r'=1$ and $s\in[\lfloor\fracν{a_-}(\frac{1}{p_-}-1) \rfloor,\infty)\cap\mathbb{Z}_+$, where $ν:=a_1+\cdots+a_n$, $a_-:=\min\{a_1,\ldots,a_n\}$, $p_-:=\min\{p_1,\ldots,p_n\}$ and, for any $t\in \mathbb{R}$, $\lfloor t\rfloor$ denotes the largest integer not greater than $t$. This duality result is new even for the isotropic mixed-norm Hardy spaces on $\mathbb{R}^n$.

math.CA↗

arXiv2018

New Calderón Reproducing Formulae with Exponential Decay on Spaces of Homogeneous Type

Assume that $(X, d, μ)$ is a space of homogeneous type in the sense of Coifman and Weiss. In this article, motivated by the breakthrough work of P. Auscher and T. Hytönen on orthonormal bases of regular wavelets on spaces of homogeneous type, the authors introduce a new kind of approximations of the identity with exponential decay (for short, $\exp$-ATI). Via such an $\exp$-ATI, motivated by another creative idea of Y. Han et al. to merge the aforementioned orthonormal bases of regular wavelets into the frame of the existed distributional theory on spaces of homogeneous type, the authors establish the homogeneous continuous/discrete Calderón reproducing formulae on $(X, d, μ)$, as well as their inhomogeneous counterparts. The novelty of this article exists in that $d$ is only assumed to be a quasi-metric and the underlying measure $μ$ a doubling measure, not necessary to satisfy the reverse doubling condition. It is well known that Calderón reproducing formulae are the cornerstone to develop analysis and, especially, harmonic analysis on spaces of homogeneous type.

math.CA↗

arXiv2018

A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type

Let $(X,d,μ)$ be a space of homogeneous type, with the upper dimension $ω$, in the sense of R. R. Coifman and G. Weiss. Assume that $η$ is the smoothness index of the wavelets on $X$ constructed by P. Auscher and T. Hytönen. In this article, when $p\in(ω/(ω+η),1]$, for the atomic Hardy spaces $H_{\mathrm{cw}}^p(X)$ introduced by Coifman and Weiss, the authors establish their various real-variable characterizations, respectively, in terms of the grand maximal function, the radial maximal function, the non-tangential maximal functions, the various Littlewood-Paley functions and wavelet functions. This completely answers the question of R. R. Coifman and G. Weiss by showing that no any additional (geometrical) condition is necessary to guarantee the radial maximal function characterization of $H_{\mathrm{cw}}^1(X)$ and even of $H_{\mathrm{cw}}^p(X)$ with $p$ as above. As applications, the authors obtain the finite atomic characterizations of $H^p_{\mathrm{cw}}(X)$, which further induce some criteria for the boundedness of sublinear operators on $H^p_{\mathrm{cw}}(X)$. Compared with the known results, the novelty of this article is that $μ$ is not assumed to satisfy the reverse doubling condition and $d$ is only a quasi-metric, moreover, the range $p\in(ω/(ω+η),1]$ is natural and optimal.

math.CA↗