Dachun Yang

Compactness and Its Applications of Sobolev Spaces Associated with Ball Banach Function Spaces

Xiaosheng Lin, Dachun Yang, Wen Yuan +1

Let $N \in N \cap [2, \infty),$ $Ω$ be a bounded Lipschitz domain in $R^{N}$ , and $X (Ω)$ be a ball Banach function space on $Ω.$ In this article, under some mild assumpt…

Variable Muckenhoupt $A_{\infty}$ Weights

Dachun Yang, Wen Yuan, Zongze Zeng

In this article, with introducing concepts of variable scalar $A_{p (\cdot), \infty}$ weights and variable matrix $A_{p (\cdot), \infty}$ weights, we seek a compreh…

Real-variable theory of function spaces with operator-valued $A_{p}$ weights in Banach spaces

Tuomas P. Hytönen, Yinqin Li, Dachun Yang +1

While the theory of matrix-weighted function spaces is well established, the majority of previous results in the infinite-dimensional operator-valued setting deal with "no go" theo…

Real-variable theory of matrix-weighted multi-parameter Besov--Triebel--Lizorkin-type spaces

Fan Bu, Yiqun Chen, Tuomas Hytönen +2

We develop a comprehensive theory for a general class of multi-parameter function spaces of Besov-Triebel-Lizorkin type, with a matrix weight. We prove the equivalence of different…

Product Hardy Spaces on Spaces of Homogeneous Type: Discrete Product Calderón-Type Reproducing Formula, Atomic Characterization, and Product Calderón--Zygmund Operators

Ziyi He, Dachun Yang, Taotao Zheng

Let $i \in {1, 2}$ and $X_{i}$ be a space of homogeneous type in the sense of Coifman and Weiss with the upper dimension $ω_{i}$ . Also let $η_{i}$ be the smoothness index of the Auscher--…

Matrix-Weighted Poincaré-Type Inequalities with Applications to Logarithmic Hajłasz--Besov Spaces on Spaces of Homogeneous Type

Ziwei Li, Dachun Yang, Wen Yuan

Let $X$ be a space of homogeneous type. In this article, based on the reducing operators of matrix $A_{p}$ -weights, the authors introduce the vector-valued Hajłasz gradi…

A Sharp Localized Weighted Inequality Related to Gagliardo and Sobolev Seminorms and Its Applications

Pingxu Hu, Yinqin Li, Dachun Yang +1

In this article, we establish a nearly sharp localized weighted inequality related to Gagliardo and Sobolev seminorms, respectively, with the sharp $A_{1}$ -weight constant or with th…

Maz'ya--Shaposhnikova Representation of Quasi-Norms of Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type with Weak Reverse Doubling Property

Eiichi Nakai, Menghao Tang, Dachun Yang +2

Let $Y (X)$ be a ball quasi-Banach function space on the space of homogeneous type $(X, ρ, μ)$ satisfying some mild additional assumptions, $q \in (0, \infty)$ , and $…

Variable Matrix-Weighted Besov Spaces

Dachun Yang, Wen Yuan, Zongze Zeng

In this article, using variable matrix $A_{p (\cdot), \infty}$ weights, we introduce the matrix-weighted variable Besov space $B_{p (\cdot), q (\cdot)}^{s (\cdot)} (W)$ and th…

Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators

Yiqun Chen, Dachun Yang, Wen Yuan

Let $p \in (0, \infty)$ , $q \in [1, \infty)$ , $s \in Z_{+}$ , and $W$ be an $A_{p}$ -matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{m a x {1, p}}$ weight. In this ar…

Characterization of Vanishing Campanato Spaces via Ball Banach Function Spaces and Its Applications

Xing Fu, Yoshihiro Sawano, Jin Tao +1

In this article, the authors provide some new characterizations of several vanishing Campanato spaces using a type of oscillation defined within the general framework of ball Banac…

Difference and Wavelet Characterizations of Distances from Functions in Lipschitz Spaces to Their Subspaces

Feng Dai, Eero Saksman, Dachun Yang +2

Let $Λ_{s}$ denote the Lipschitz space of order $s \in (0, \infty)$ on $R^{n}$ , which consists of all $f \in C \cap L^{\infty}$ such that, for some constant $L\in(0,\infty)…

Sharp Brezis--Seeger--Van Schaftingen--Yung Formulae for Higher-Order Gradients in Ball Banach Function Spaces

Pingxu Hu, Yinqin Li, Dachun Yang +2

Let $X$ be a ball Banach function space on $R^{n}$ , $k \in N$ , $h \in R^{n}$ , and $Δ_{h}^{k}$ denote the $k$ {\rm th} order difference. In this article, under some mi…

Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators

Dachun Yang, Wen Yuan, Mingdong Zhang

This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $A_{\infty}$ weights. In this article, we estab…

Matrix-Weighted Besov-Triebel-Lizorkin Spaces of Optimal Scale: Real-Variable Characterizations, Invariance on Integrable Index, and Sobolev-Type Embedding

Fan Bu, Dachun Yang, Wen Yuan +1

In this article, using growth functions we introduce generalized matrix-weighted Besov-Triebel-Lizorkin-type spaces with matrix $A_{\infty}$ weights. We first characteriz…

Parabolic Extrapolation and Its Applications to Characterizing Parabolic BMO Spaces via Parabolic Fractional Commutators

Mingming Cao, Weiyi Kong, Dachun Yang +2

In this article, we establish the parabolic version of the celebrated Rubio de Francia extrapolation theorem. As applications, we obtain new characterizations of parabolic BMO-type…

Maximal Function and Atomic Characterizations of Matrix-Weighted Hardy Spaces with Their Applications to Boundedness of Calderón--Zygmund Operators

Fan Bu, Yiqun Chen, Dachun Yang +1

Let $p \in (0, 1]$ and $W$ be an $A_{p}$ -matrix weight, which in scalar case is exactly a Muckenhoupt $A_{1}$ weight. In this article, we introduce matrix-weighted Hardy spaces $H_{W}^{p}$ vi…

math.FA2024

Regularity of Characteristic Functions in Besov-Type and Triebel--Lizorkin-Type Spaces

Wen Yuan, Winfried Sickel, Dachun Yang

In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel--Lizorkin-type spaces under restrictions on the measure of the $…

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces III: Characterizations of Molecules and Wavelets, Trace Theorems, and Boundedness of Pseudo-Differential Operators and Calderón--Zygmund Operators

Fan Bu, Tuomas Hytönen, Dachun Yang +1

This is the last one of three successive articles by the authors on matrix-weighted Besov-type and Triebel--Lizorkin-type spaces $B ˙_{p, q}^{s, τ} (W)$ and $F ˙_{p, q}^{s, τ} (W)$ …

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces II: Sharp Boundedness of Almost Diagonal Operators

Fan Bu, Tuomas Hytönen, Dachun Yang +1

This article is the second one of three successive articles of the authors on the matrix-weighted Besov-type and Triebel--Lizorkin-type spaces. In this article, we obtain the sharp…

New Characterizations and Properties of Matrix $A_{\infty}$ Weights

Fan Bu, Tuomas Hytönen, Dachun Yang +1

We provide several new characterizations of $A_{p, \infty}$ -matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_{\infty}$ weights. In…