Fan Bu

activity

20232026

collaborators

10 papers

math.CA2026

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Fan Bu, Dachun Yang, Wen Yuan

Let $T$ be a convolution Calderón--Zygmund operator satisfying Hytönen's non-degeneracy condition. We prove that, for every $p \in (1, \infty)$ and $m \geq 3$ , there exists a positive co…

math.CA2026

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights

Fan Bu, Shuaijun Feng, Qingying Xue +2

Let $α \in R$ , $p \in (0, \infty)$ , and $q \in (0, \infty]$ . In this article, we develop a theory of matrix-weighted anisotropic Besov spaces associated with an expansive matrix $…

math.FA2026

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…

math.FA2025

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…

math.FA2025

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.FA2025

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_{\infty}$ Weights

Fan Bu, Tuomas Hytönen, Dachun Yang +1

Introduced by A. Volberg, matrix $A_{p, \infty}$ weights provide a suitable generalization of Muckenhoupt $A_{\infty}$ weights from the classical theory. In our previous work, we esta…

math.FA2023

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 $F ˙_{p, q}^{s, τ} (W)$ …

math.FA2023

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…

math.FA2023

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…

math.FA2023

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces I: $A_{p}$ -Dimensions of Matrix Weights and $φ$ -Transform Characterizations

Fan Bu, Tuomas P. Hytönen, Dachun Yang +1

Let $s \in R$ , $q \in (0, \infty]$ , and $τ \in [0, \infty)$ . It is well known that Besov-type spaces $B ˙_{p, q}^{s, τ}$ with $p \in (0, \infty]$ and Triebel--Lizorkin-type space…

Sharp Matrix-Weighted Lower Bounds for Non-Degenerate Convolution Calderón--Zygmund Operators

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix A∞​ Weights

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

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

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

Besov--Triebel--Lizorkin-Type Spaces with Matrix A∞​ Weights

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

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

New Characterizations and Properties of Matrix A∞​ Weights

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces I: Ap​-Dimensions of Matrix Weights and φ-Transform Characterizations

Real-Variable Characterizations and Their Applications of Anisotropic Besov Spaces with Matrix $A_{\infty}$ Weights

Besov--Triebel--Lizorkin-Type Spaces with Matrix $A_{\infty}$ Weights

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

Matrix-Weighted Besov-Type and Triebel--Lizorkin-Type Spaces I: $A_{p}$ -Dimensions of Matrix Weights and $φ$ -Transform Characterizations