16 papers · 1 filter
Real-variable theory of function spaces with operator-valued 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 and be a space of homogeneous type in the sense of Coifman and Weiss with the upper dimension . Also let 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 be a space of homogeneous type. In this article, based on the reducing operators of matrix -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 -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 be a ball quasi-Banach function space on the space of homogeneous type satisfying some mild additional assumptions, , and $…