Huo-xiong Wu

activity

20132026

most citedA revisit on the compactness of commutators

23 citations · 64 across the 26 of their papers we have counts for

collaborators

27 papers

cs.AI2026

RECAP: Calibrating Low-Bit Reasoning Models on the History They Read

Chi Ruan, Yujie Chen, Zixiang Zhao +2

Low-bit quantization reduces the cost of serving reasoning models but can substantially degrade long chains of thought. Each step reads cached keys and values spanning thousands of…

math.FA2023

Commutators for certain fractional type operators on weighted spaces and Orlicz-Morrey spaces

Huoxiong Wu Tong Zhang

In this paper, we focus on a class of fractional type integral operators that can be served as extensions of Riesz potential with kernels $$K(x,y)=\frac{Ω_1(x-A_1 y)}{|x-A_1 y |^{\…

math.AP2023

Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces

Guoxia Feng, Manli Song, Huoxiong Wu

Assume that $(X, d, μ)$ is a metric space endowed with a non-negative Borel measure $μ$ satisfying the doubling condition and the additional condition that $μ (B (x, r)) ≳ r^{n}$ for…

math.AP2021

Well-posedness of Navier-Stokes equations established by the decaying speed of single norm

Qixiang Yang, Huoxiong Wu, Jianxun He +1

The decaying speed of a single norm more truly reflects the intrinsic harmonic analysis structure of the solution of the classical incompressible Navier-Stokes equations. No previo…

math.CA2021

On the Bounds of Weak $(1, 1)$ Norm of Hardy-Littlewood Maximal Operator with $L lo g L (S^{n - 1})$ Kernels

Moyan Qin, Huoxiong Wu, Qingying Xue

Let $Ω \in L^{1} (S^{n - 1})$ , be a function of homogeneous of degree zero, and $M_{Ω}$ be the Hardy-Littlewood maximal operator associated with $Ω$ defined by $M_Ω(f)(x) = \su…

math.AP2021

A remark on ill-posedness

Haibo Yang, Qixiang Yang, Huoxiong Wu

Norm inflation implies certain discontinuous dependence of the solution on the initial value. The well-posedness of the mild solution means the existence and uniqueness of the fixe…

math.CA2021

Bump conditions and two-weight inequalities for commutators of fractional integrals

Yongming Wen, Huoxiong Wu

This paper gives new two-weight bump conditions for the sparse operators related to iterated commutators of fractional integrals. As applications, the two-weight bounds for iterate…

math.CA2021

Limiting weak-type behaviors for singular integrals with rough $L lo g L (S^{n})$ kernels

Moyan Qin, Huoxiong Wu, Qingying Xue

Let $Ω$ be a function of homogeneous of degree zero and vanish on the unit sphere $S^{n}$ . In this paper, we investigate the limiting weak-type behavior for singular integr…

math.AP2021

A note on extrapolation of compactness

Shenyu Liu, Huoxiong Wu, Dongyong Yang

This note is devoted to the study of Hytönen's extrapolation theorem of compactness on weighted Lebesgue spaces. Two criteria of compactness of linear operators in the two-weight s…

math.CA2021

The limiting weak type behaviors and The lower bound for a new weak $L lo g L$ type norm of strong maximal operators

Moyan Qin, Huoxiong Wu, Qingying Xue

It is well known that the weak ( $1, 1$ ) bounds doesn't hold for the strong maximal operators, but it still enjoys certain weak $L lo g L$ type norm inequality. Let $Φ_n(t)=t(1+(\log^…

math.CA2020

Limiting weak-type behavior for rough bilinear operators

Moyan Qin, Huoxiong Wu, Qingying Xue

Let $Ω_{1}, Ω_{2}$ be functions of homogeneous of degree $0$ and $Ω = (Ω_{1}, Ω_{2}) \in L lo g L (S^{n - 1}) \times L lo g L (S^{n - 1})$ . In this paper, we investigate the limiti…

math.CA2020★ 1 cited

Variational characterizations of weighted Hardy spaces and weighted $B M O$ spaces

Weichao Guo, Yongming Wen, Huoxiong Wu +1

This paper obtains new characterizations of weighted Hardy spaces and certain weighted $B M O$ type spaces via the boundedness of variation operators associated with approximate iden…

math.CA2019

On the compactness of oscillation and variation of commutators

Weichao Guo, Yongming Wen, Huoxiong Wu +1

In this paper, we first establish the weighted compactness result for oscillation and variation associated with the truncated commutator of singular integral operators. Moreover, w…

math.CA2018★ 1 cited

Boundedness and compactness of commutators associated with Lipschitz functions

Weichao Guo, Jianxun He, Huoxiong Wu +1

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…

math.CA2017★ 23 cited

A revisit on the compactness of commutators

Weichao Guo, Huoxiong Wu, Dongyong Yang

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…

math.CA2017★ 2 cited

Limiting weak-type behaviors of some integral operators

Weichao Guo, Jianxun He, Huoxiong Wu

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…

math.CA2017★ 7 cited

The unified theory for the necessity of bounded commutators and applications

Weichao Guo, Jiali Lian, Huoxiong Wu

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…

math-ph2017

Ill-posedness of Naiver-Stokes equations and critical Besov-Morrey spaces

Qixiang Yang, Haibo Yang, Huoxiong Wu

The blow up phenomenon in the first step of the classical Picard's scheme was proved in this paper. For certain initial spaces, Bourgain-Pavlović and Yoneda proved the ill-posednes…

math.CA2016

Characterization of inclusion relations between wiener amalgam and some classical spaces

Weichao Guo, Huoxiong Wu, Qixiang Yang +1

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 inclus…

math.CA2016

Inclusion relations between Modulation and Triebel-Lizorkin spaces

Weichao Guo, Huoxiong Wu, Guoping Zhao

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 im…

math.CA2016★ 1 cited

Full Characterization of embedding relations between alpha modulation spaces

Weichao Guo, Dashan Fan, Huoxiong Wu +1

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 a…

math.AP2016

Oscillation and variation for semigroups associated with Bessel operators

Huoxiong Wu, Dongyong Yang, Jing Zhang

Let $λ > 0$ and $△_{λ} := - \frac{d ^{2}}{d x ^{2}} - \frac{2 λ}{x} \frac{d}{d x}$ be the Bessel operator on $R_{+} := (0, \infty)$ . We show that the oscillation operator ${\mathcal O(P^{[…

math.AP2016★ 2 cited

Oscillation and variation for Riesz transform associated with Bessel operators

Huoxiong Wu, Dongyong Yang, Jing Zhang

Let $λ > 0$ and $△_{λ} := - \frac{d ^{2}}{d x ^{2}} - \frac{2 λ}{x} \frac{d}{d x}$ be the Bessel operator on $R_{+} := (0, \infty)$ . We show that the oscillation operator $\mathcal{O}(R_{Δ…

math.CA2016★ 1 cited

Compactness of Riesz transform commutator associated with Bessel operators

Xuan Thinh Duong, Ji Li, Suzhen Mao +2

Let $λ > 0$ and $△_{λ} := - \frac{d ^{2}}{d x ^{2}} - \frac{2 λ}{x} \frac{d}{d x}$ be the Bessel operator on $R_{+} := (0, \infty)$ . We first introduce and obtain an equivalent characteriz…

RECAP: Calibrating Low-Bit Reasoning Models on the History They Read

Commutators for certain fractional type operators on weighted spaces and Orlicz-Morrey spaces

Decay estimates for a class of semigroups related to self-adjoint operators on metric measure spaces

Well-posedness of Navier-Stokes equations established by the decaying speed of single norm

On the Bounds of Weak (1,1) Norm of Hardy-Littlewood Maximal Operator with LlogL(Sn−1) Kernels

A remark on ill-posedness

Bump conditions and two-weight inequalities for commutators of fractional integrals

Limiting weak-type behaviors for singular integrals with rough LlogL(Sn) kernels

A note on extrapolation of compactness

The limiting weak type behaviors and The lower bound for a new weak LlogL type norm of strong maximal operators

Limiting weak-type behavior for rough bilinear operators

Variational characterizations of weighted Hardy spaces and weighted BMO spaces

On the compactness of oscillation and variation of commutators

Boundedness and compactness of commutators associated with Lipschitz functions

A revisit on the compactness of commutators

Limiting weak-type behaviors of some integral operators

The unified theory for the necessity of bounded commutators and applications

Ill-posedness of Naiver-Stokes equations and critical Besov-Morrey spaces

Characterization of inclusion relations between wiener amalgam and some classical spaces

Inclusion relations between Modulation and Triebel-Lizorkin spaces

Full Characterization of embedding relations between alpha modulation spaces

Oscillation and variation for semigroups associated with Bessel operators

Oscillation and variation for Riesz transform associated with Bessel operators

Compactness of Riesz transform commutator associated with Bessel operators

On the Bounds of Weak $(1, 1)$ Norm of Hardy-Littlewood Maximal Operator with $L lo g L (S^{n - 1})$ Kernels

Limiting weak-type behaviors for singular integrals with rough $L lo g L (S^{n})$ kernels

The limiting weak type behaviors and The lower bound for a new weak $L lo g L$ type norm of strong maximal operators

Variational characterizations of weighted Hardy spaces and weighted $B M O$ spaces