arXiv subjects

Lian Wu

Publications and source records attributed to Lian Wu.

16 recordsLinked to original sources

arXiv2026

Sharp weighted norm estimates for martingale square functions

This paper is devoted to the study of quantitative weighted norm estimates for martingale square functions in both scalar-weighted and matrix-weighted settings. In particular, we introduce the martingale square functions $S_W$ via matrix weights $W$, and then use the matrix $A_p$ condition, introduced in our previous work \cite{ChenQuanJiaoWu}, to characterize the $L_p$ estimate for $S_W$. Our proof mainly relies on the idea of sparse dominations, which leads to the explicit information on the characteristic of the matrix weight involved. For the range $1<p\leq 2$, our result is sharp in terms of the characteristic of the matrix weight. With some modification on the arguments, we can further improve the result in scalar settings by obtaining the optimal exponent of the characteristic of the weight involved for all indices $1<p<\infty$, addressing a fundamental problem from the classical martingale theory.

math.PR↗

arXiv2025

Base-Detail Feature Learning Framework for Visible-Infrared Person Re-Identification

Visible-infrared person re-identification (VIReID) provides a solution for ReID tasks in 24-hour scenarios; however, significant challenges persist in achieving satisfactory performance due to the substantial discrepancies between visible (VIS) and infrared (IR) modalities. Existing methods inadequately leverage information from different modalities, primarily focusing on digging distinguishing features from modality-shared information while neglecting modality-specific details. To fully utilize differentiated minutiae, we propose a Base-Detail Feature Learning Framework (BDLF) that enhances the learning of both base and detail knowledge, thereby capitalizing on both modality-shared and modality-specific information. Specifically, the proposed BDLF mines detail and base features through a lossless detail feature extraction module and a complementary base embedding generation mechanism, respectively, supported by a novel correlation restriction method that ensures the features gained by BDLF enrich both detail and base knowledge across VIS and IR features. Comprehensive experiments conducted on the SYSU-MM01, RegDB, and LLCM datasets validate the effectiveness of BDLF.

cs.CV↗

arXiv2025

Weighted norm estimates of noncommutative Calder\'{o}n-Zygmund operators

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type $(1,1)$ estimate of noncommutative maximal Calder\'{o}n-Zygmund operators, corresponding version of square functions and a weighted $H_1- L_1$ type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt $A_1$ class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.

math.OA↗

arXiv2023

Asymmetric Burkholder inequalities in noncommutative symmetric spaces

In this paper, we establish noncommutative Burkholder inequalities with asymmetric diagonals in symmetric operator spaces. Our proof mainly relies on a new complex interpolation result on asymmetric vector valued spaces and a duality approach. We include as well the asymmetric versions of noncommutative Johnson-Schechtman inequalities.

math.OA↗

arXiv2022

The sharp weighted maximal inequalities for noncommutative martingales

The purpose of the paper is to establish weighted maximal $L_p$-inequalities in the context of operator-valued martingales on semifinite von Neumann algebras. The main emphasis is put on the optimal dependence of the $L_p$ constants on the characteristic of the weight involved. As applications, we establish weighted estimates for the noncommutative version of Hardy-Littlewood maximal operator and weighted bounds for noncommutative maximal truncations of a wide class of singular integrals.

math.OA↗

arXiv2021

Secure Your Ride: Real-time Matching Success Rate Prediction for Passenger-Driver Pairs

In recent years, online ride-hailing platforms have become an indispensable part of urban transportation. After a passenger is matched up with a driver by the platform, both the passenger and the driver have the freedom to simply accept or cancel a ride with one click. Hence, accurately predicting whether a passenger-driver pair is a good match turns out to be crucial for ride-hailing platforms to devise instant order assignments. However, since the users of ride-hailing platforms consist of two parties, decision-making needs to simultaneously account for the dynamics from both the driver and the passenger sides. This makes it more challenging than traditional online advertising tasks. Moreover, the amount of available data is severely imbalanced across different cities, creating difficulties for training an accurate model for smaller cities with scarce data. Though a sophisticated neural network architecture can help improve the prediction accuracy under data scarcity, the overly complex design will impede the model's capacity of delivering timely predictions in a production environment. In the paper, to accurately predict the MSR of passenger-driver, we propose the Multi-View model (MV) which comprehensively learns the interactions among the dynamic features of the passenger, driver, trip order, as well as context. Regarding the data imbalance problem, we further design the Knowledge Distillation framework (KD) to supplement the model's predictive power for smaller cities using the knowledge from cities with denser data and also generate a simple model to support efficient deployment. Finally, we conduct extensive experiments on real-world datasets from several different cities, which demonstrates the superiority of our solution.

cs.LG↗

arXiv2021

Distributional inequalities for noncommutative martingales

We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include distributional versions of the noncommutative Stein, dual Doob, martingale transform and Burkholder-Gundy inequalities. Our proof relies upon new and powerful extrapolation theorems. As an application, we obtain some new martingale inequalities in symmetric quasi-Banach operator spaces and some interesting endpoint estimates. Our main approach demonstrates a method to build the noncommutative and classical probabilistic inequalities in an entirely operator theoretic way.

math.FA↗

arXiv2020

Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis

Let $p(\cdot)$ be a measurable function defined on a probability space satisfying $0 1$. The boundedness of the maximal Fej{é}r operator on $H_{p(\cdot)}$ and $H_{p(\cdot),q}$ is proved whenever $p_->1/2$ and the condition $\frac{1}{p_-}-\frac{1}{p_+} <1$ hold. It is surprising that this last condition does not appear for trigonometric Fourier series. One of the key points of the proof is that we introduce two new dyadic maximal operators and prove their boundedness on $L_{p(\cdot)}$ with $p_->1$. The method we use to prove these results is new even in the classical case. As a consequence, we obtain theorems about almost everywhere and norm convergence of the Fejér means.

math.PR↗

arXiv2019

Square functions for noncommutative differentially subordinate martingales

We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if $x$ is a self-adjoint noncommutative martingale and $y$ is weakly differentially subordinate to $x$ then $y$ admits a decomposition $dy=a +b +c$ (resp. $dy=z +w$) where $a$, $b$, and $c$ are adapted sequences (resp. $z$ and $w$ are martingale difference sequences) such that: $$ \Big\| (a_n)_{n\geq 1}\Big\|_{L_{1,\infty}({\mathcal M}\overline{\otimes}\ell_\infty)} +\Big\| \Big(\sum_{n\geq 1} \mathcal{E}_{n-1}|b_n|^2 \Big)^{{1}/{2}}\Big\|_{1, \infty} + \Big\| \Big(\sum_{n\geq 1} \mathcal{E}_{n-1}|c_n^*|^2 \Big)^{{1}/{2}}\Big\|_{1, \infty} \leq C\big\| x \big\|_1 $$ (resp. $$ \Big\| \Big(\sum_{n\geq1} |z_n|^2 \Big)^{{1}/{2}}\Big\|_{1, \infty} + \Big\| \Big(\sum_{n\geq 1} |w_n^*|^2 \Big)^{{1}/{2}}\Big\|_{1, \infty} \leq C\big\| x \big\|_1). $$ We also prove strong-type $(p,p)$ versions of the above weak-type results for $1<p<2$. In order to provide more insights into the interactions between noncommutative differential subordinations and martingale Hardy spaces when $1\leq p<2$, we also provide several martingale inequalities with sharp constants which are new and of independent interest. As a byproduct of our approach, we obtain new and constructive proofs of both the noncommutative Burkholder-Gundy inequalities and the noncommutative Burkholder/Rosenthal inequalities for $1<p<2$ with the optimal order of the constants when $p \to 1$.

math.OA↗

arXiv2018

Noncommutative Good-$\lambda$ Inequalities

We propose a novel approach in noncommutative probability, which can be regarded as an analogue of good-$\lambda$ inequalities from the classical case due to Burkholder and Gundy (Acta Math {\bf124}: 249-304,1970). This resolves a longstanding open problem in noncommutative realm. Using this technique, we present new proofs of noncommutative Burkholder-Gundy inequalities, Stein's inequality, Doob's inequality and $L^p$-bounds for martingale transforms; all the constants obtained are of optimal orders. The approach also allows us to investigate the noncommutative analogues of decoupling techniques and, in particular, to obtain new estimates for noncommutative martingales with tangent difference sequences and sums of tangent positive operators. These in turn yield an enhanced version of Doob's maximal inequality for adapted sequences and a sharp estimate for a certain class of Schur multipliers. We also present fully new applications of good-$\lambda$ approach to noncommutative harmonic analysis, including inequalities for differentially subordinate operators motivated by the classical $L^p$-bound for the Hilbert transform and the estimate for the $j$-th Riesz transform on group von Neumann algebras with constants of optimal orders as $p\to\infty.$

math.OA↗

arXiv2017

Noncommutative Davis type decompositions and applications

We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $Φ$-moment Burkholder/Rosenthal inequality for Orlicz functions that are either $p$-convex and $2$-concave for some $1<p<2$ or are $2$-convex and $q$-concave for some $2<q<\infty$.

math.PR↗

arXiv2015

Noncommutative Burkholder/Rosenthal inequalities associated with convex functions

We prove noncommutative martingale inequalities associated with convex functions. More precisely, we obtain $Φ$-moment analogues of the noncommutative Burkholder inequalities and the noncommutative Rosenthal inequalities for any convex Orlicz function $Φ$ whose Matuzewska-Orlicz indices $p_Φ$ and $q_Φ$ are such that $1<p_Φ\leq q_Φ<2$ or $2<p_Φ\leq q_Φ<\infty$. These results generalize the noncommutative Burkholder/Rosenthal inequalities due to Junge and Xu.

math.PR↗

arXiv2015

Martingale inequalities in noncommutative symmetric spaces

We provide generalizations of Burkholder's inequalities involving conditioned square functions of martingales to the general context of martingales in noncommutative symmetric spaces. More precisely, we prove that Burkholder's inequalities are valid for any martingale in noncommutative space constructed from a symmetric space defined on the interval $(0,\infty)$ with Fatou property and whose Boyd indices are strictly between 1 and 2. This answers positively a question raised by Jiao and may be viewed as a conditioned version of similar inequalities for square functions of noncommutative martingales. Using duality, we also recover the previously known case where the Boyd indices are finite and are strictly larger than 2.

math.OA↗

arXiv2015

Noncommutative Fractional integrals

Let $\M$ be a hyperfinite finite von Nemann algebra and $(\M_k)_{k\geq 1}$ be an increasing filtration of finite dimensional von Neumann subalgebras of $\M$. We investigate abstract fractional integrals associated to the filtration $(\M_k)_{k\geq 1}$. For a finite noncommutative martingale $x=(x_k)_{1\leq k\leq n} \subseteq L_1(\M)$ adapted to $(\M_k)_{k\geq 1}$ and $0<α<1$, the fractional integral of $x$ of order $α$ is defined by setting: $$I^αx = \sum_{k=1}^n ζ_k^α dx_k$$ for an appropriate sequence of scalars $(ζ_k)_{k\geq 1}$. For the case of noncommutative dyadic martingale in $L_1(\R)$ where $\R$ is the type ${\rm II}_1$ hyperfinite factor equipped with its natural increasing filtration, $ζ_k=2^{-k}$ for $k\geq 1$. We prove that $I^α$ is of weak-type $(1, 1/(1-α))$. More precisely, there is a constant ${\mathrm c}$ depending only on $α$ such that if $x=(x_k)_{k\geq 1}$ is a finite noncommutative martingale in $L_1(\M)$ then \[\|I^αx\|_{L_{1/(1-α),\infty}(\mathcal{\M})}\leq {\mathrm c}\|x\|_{L_1(\M)}.\] We also obtain that $I^α$ is bounded from $L_{p}(\M)$ into $L_{q}(\M)$ where $1<p<q<\infty$ and $α=1/p-1/q$, thus providing a noncommutative analogue of a classical result. Furthermore, we investigate the corresponding result for noncommutative martingale Hardy spaces. Namely, there is a constant ${\mathrm c}$ depending only on $α$ such that if $x=(x_k)_{k\geq 1}$ is a finite noncommutative martingale in the martingale Hardy space $\mathcal{H}_1(\M)$ then $\|I^αx\|_{\mathcal{H}_{1/(1-α)}(\M)}\leq {\mathrm c} \|x\|_{\mathcal{H}_1(\M)}$.

math.OA↗

arXiv2014

The predual and John-Nirenberg inequalities on generalized BMO martingale spaces

In this paper we introduce the generalized BMO martingale spaces by stopping time sequences, which enable us to characterize the dual spaces of martingale Hardy-Lorentz spaces $H_{p,q}^s$ for $0<p\leq1, 1<q<\infty$. Moreover, by duality we obtain a John-Nirenberg theorem for the generalized BMO martingale spaces when the stochastic basis is regular. We also extend the boundedness of fractional integrals to martingale Hardy-Lorentz spaces.

math.FA↗

arXiv2013

Weak Orlicz-Hardy Martingale Spaces

In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient condition for a sublinear operator defined on the weak Orlicz-Hardy martingale spaces to be bounded is given. Further, we investigate the duality of weak Orlicz-Hardy martingale spaces and obtain a new John-Nirenberg type inequality when the stochastic basis is regular. These results can be regarded as weak versions of the Orlicz-Hardy martingale spaces due to Miyamoto, Nakai and Sadasue.

math.FA↗