Dachun Yang

Morrey and Campanato meet Besov, Lizorkin and Triebel

During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p =

A Theory of Besov and Triebel-Lizorkin Spaces on Metric Measure Spaces Modeled on Carnot-Carathéodory Spaces

We work on RD-spaces 𝒳 , namely, spaces of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in 𝒳 . An important example is the Carnot-Caratheodory space with doubling measure. By constructing an approximation of the identity with bounded support of Coifman type, we develop a theory of Besov and Triebel-Lizorkin spaces on the underlying spaces. In particular, this includes a theory of Hardy spaces H p ( 𝒳 ) and local Hardy spaces h p ( 𝒳 ) on RD-spaces, which appears to be new in this setting. Among other things, we give frame characterization of these function spaces, study interpolation of such spaces by the real method, and determine their dual spaces when p ≥ 1 . The relations among homogeneous Besov spaces and Triebel-Lizorkin spaces, inhomogeneous Besov spaces and Triebel-Lizorkin spaces, Hardy spaces, and BMO are also presented. Moreover, we prove boundedness results on these Besov and Triebel-Lizorkin spaces for classes of singular integral operators, which include non-isotropic smoothing operators of order zero in the sense of Nagel and Stein that appear in estimates for solutions of the Kohn-Laplacian on certain classes of model domains in ℂ N . Our theory applies in a wide range of settings.

The Hardy space H 1 on non-homogeneous metric spaces

Academy of Finland [130166, 133264, 218148]; National Natural Science Foundation of China [11171027, 11101339]; Program for Changjiang Scholars and Innovative Research Team at the University of China

Local Hardy spaces of Musielak-Orlicz type and their applications

Let φ: ℝn × [0,∞) → [0,∞) be a function such that φ(x, ·) is an Orlicz function and

Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generalized Carleson measure spaces

\phi ( \cdot ,t) \in \mathbb{A}_\infty ^{loc} \left( {\mathbb{R}^n } \right)

Interpolation of Morrey-Campanato and related smoothness spaces

(the class of local weights introduced by Rychkov). In this paper, the authors introduce a local Musielak-Orlicz Hardy space hφ(ℝn) by the local grand maximal function, and a local BMO-type space bmoφ(ℝn) which is further proved to be the dual space of hφ(ℝn). As an application, the authors prove that the class of pointwise multipliers for the local BMO-type space bmoφ(ℝn), characterized by Nakai and Yabuta, is just the dual of

Bilinear operators on Herz-type Hardy spaces

L^1 \left( {\mathbb{R}^n } \right) + h_{\Phi _0 } \left( {\mathbb{R}^n } \right)