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Weichao Guo

Publications and source records attributed to Weichao Guo.

31 records · Page 2Linked to original sources
arXiv2018

Sharp estimates of unimodular Fourier multipliers on Wiener amalgam spaces

We study the boundedness on the Wiener amalgam spaces $W^{p,q}_s$ of Fourier multipliers with symbols of the type $e^{iμ(ξ)}$, for some real-valued functions $μ(ξ)$ whose prototype is $|ξ|^β$ with $β\in (0,2]$. Under some suitable assumptions on $μ$, we give the characterization of $W^{p,q}_s\rightarrow W^{p,q}$ boundedness of $e^{iμ(D)}$, for arbitrary pairs of $0< p,q\leq \infty$. Our results are an essential improvement of the previous known results, for both sides of sufficiency and necessity, even for the special case $μ(ξ)=|ξ|^β$ with $1<β<2$.

math.CA↗
arXiv2018

Hausdorff operators on the Sobolev spaces $W^{k,1}$

This paper is served as a first contribution regarding the boundedness of Hausdorff operators on function spaces with smoothness. The sharp conditions are established for boundedness of Hausdorff operators on Sobolev spaces $W^{k,1}$. As applications, some bounded and unbounded properties of Hardy operator and adjoint Hardy operator on $W^{k,1}$ are deduced.

math.CA↗
arXiv2018

Boundedness and compactness of commutators associated with Lipschitz functions

Let $α\in (0, 1]$, $β\in [0, n)$ and $T_{Ω,β}$ be a singular or fractional integral operator with homogeneous kernel $Ω$. In this article, a CMO type space ${\rm CMO}_α(\mathbb R^n)$ is introduced and studied. In particular, the relationship between ${\rm CMO}_α(\mathbb R^n)$ and the Lipchitz space $Lip_α(\mathbb R^n)$ is discussed. Moreover, a necessary condition of restricted boundedness of the iterated commutator $(T_{Ω,β})^m_b$ on weighted Lebesgue spaces via functions in $Lip_α(\mathbb R^n)$, and an equivalent characterization of the compactness for $(T_{Ω,β})^m_b$ via functions in ${\rm CMO}_α(\mathbb R^n)$ are obtained. Some results are new even in the unweighted setting for the first order commutators.

math.CA↗
arXiv2017

A revisit on the compactness of commutators

A new characterization of CMO(R^n) is established by the local mean oscillation. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.

math.CA↗
arXiv2017

Limiting weak-type behaviors of some integral operators

In this paper, we explore the limiting weak-type behaviors of some integral operators including maximal operators, singular and fractional integral operators and maximal truncated singular integrals et al. Some optimal limiting weak-type behaviors are given, which essentially improve and extend the previous results in this topics.

math.CA↗
arXiv2017

The unified theory for the necessity of bounded commutators and applications

The general methods which are powerful for the necessity of bounded commutators are given. As applications, some necessary conditions for bounded commutators are first obtained in certain endpoint cases, and several new characterizations of $BMO$ space, Lipschitz spaces and their weighted versions via boundedness of commutators in various function spaces are deduced.

math.CA↗
arXiv2017

Sharp Weighted Convolution Inequalities and Some Applications

In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are characterized, we also obtain the weakest conditions for the boundedness of bilinear Fourier multipliers on modulation spaces in some sense. For the fractional integral operator, the sharp conditions for the boundedness of power weighted Lp-Lq estimates in both continuous case and discrete case are obtained. By a quite different approach from others, our theorems optimize some previous results which are committed to finding sharp conditions for some classical convolution inequalities.

math.CA↗
arXiv2016

Characterization of inclusion relations between wiener amalgam and some classical spaces

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also obtain the optimal inclusion relations between local hardy spaces $h^p$ and Wiener amalgam spaces $W_{p,q}^s$, which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [J. Funct. Anal. 268 (2015), 239-254]. In addition, we establish some mild characterizations of inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces, which relates some modern inequalities to classical inequalities.

math.CA↗
arXiv2016

Inclusion relations between Modulation and Triebel-Lizorkin spaces

In this paper, we obtain the sharp conditions of the inclusion relations between modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for $p\leq 1$, which greatly improve and extend the results for the embedding relations between local Hardy spaces and modulation spaces obtained by Kobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].

math.CA↗
arXiv2016

Full Characterization of embedding relations between alpha modulation spaces

In this paper, we consider the embedding relations between any two $α$% -modulation spaces. Based on an observation that the $α$-modulation space with smaller $α$ can be regarded as a corresponding $α$% -modulation space with larger $α$, we give a complete characterization of the Fourier multipliers between $α$-modulation spaces with different $α$. Then we establish a full version of optimal embedding relations between $α$-modulation spaces. As an application, we determine that the bounded operators commuting with translations between $α$-modulation spaces are of convolution type.

math.CA↗
arXiv2016

Characterization of Some Properties on Weighted Modulation Spaces

In this paper, some properties on weighted modulation and Wiener amalgam spaces are characterized by the corresponding properties on weighted Lebesgue spaces. As applications, sharp conditions for product inequalities, convolution inequalities and embedding on weighted modulation and Wiener amalgam spaces are obtained. These applications improve and extend many known results.

math.CA↗