Dachun Yang
Beijing Normal University
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Archive | 2010
Wen Yuan; Winfried Sickel; Dachun Yang
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 =
Abstract and Applied Analysis | 2008
Yongsheng Han; Detlef Müller; Dachun Yang
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.
arXiv: Classical Analysis and ODEs | 2012
Tuomas P. Hytönen; Dachun Yang; Dongyong Yang
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
Science China-mathematics | 2012
Dachun Yang; Sibei Yang
Let φ: ℝn × [0,∞) → [0,∞) be a function such that φ(x, ·) is an Orlicz function and
Communications in Contemporary Mathematics | 2013
Shaoxiong Hou; Dachun Yang; Sibei Yang
Applicable Analysis | 2013
Dachun Yang; Wen Yuan
\phi ( \cdot ,t) \in \mathbb{A}_\infty ^{loc} \left( {\mathbb{R}^n } \right)
Analysis Mathematica | 2002
Guozhen Lu; Shanzhen Lu; Dachun Yang
Science China-mathematics | 2015
Wen Yuan; Winfried Sickel; Dachun Yang
(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
Science China-mathematics | 1997
Shanzhen Lu; Dachun Yang
Transactions of the American Mathematical Society | 1998
Loukas Grafakos; Xinwei Li; Dachun Yang
L^1 \left( {\mathbb{R}^n } \right) + h_{\Phi _0 } \left( {\mathbb{R}^n } \right)