𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Atomic decomposition for weighted Besov and Triebel-Lizorkin spaces

✍ Scribed by Mitsuo Izuki; Yoshihiro Sawano

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
250 KB
Volume
285
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Rychkov defined weighted Besov spaces and weighted Triebel‐Lizorkin spaces coming with a weight in the class \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$A_p^{\rm loc}$\end{document}, which is even wider than the class A~p~ due to Muckenhoupt. In the present paper we are concerned with the atomic decomposition of these spaces. As an application, we obtain some key theorems in the theory of function spaces. Finally we conclude this paper with some helpful examples showing the difference between weighted spaces and unweighted spaces.

📜 SIMILAR VOLUMES

Realizations of homogeneous Besov and Li
Realizations of homogeneous Besov and Lizorkin-Triebel spaces
✍ Gérard Bourdaud 📂 Article 📅 2012 🏛 John Wiley and Sons 🌐 English ⚖ 236 KB

## Abstract We discuss the existence and unicity of translation and dilation commuting realizations of the homogeneous spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\dot{B}\_{{p},{q}}^{s}({\mathbb R}^n\!)$\end{document} and \documentclass{article}\usepackage{am

Besov-Morrey spaces and Triebel-Lizorkin
Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces for nondoubling measures
✍ Yoshihiro Sawano; Hitoshi Tanaka 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 252 KB

## Abstract We define Morrey type Besov‐Triebel spaces with the underlying measure non‐doubling. After defining the function spaces, we investigate boundedness property of some class of the singular integral operators (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Besov-Morrey spaces and Triebel-Lizorkin
Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces on domains
✍ Yoshihiro Sawano 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 294 KB

## Abstract The purpose of this paper is to develop a theory of the Besov‐Morrey spaces and the Triebel‐Lizorkin‐Morrey spaces on domains in **R**^__n__^. We consider the pointwise multiplier operator, the trace operator, the extension operator and the diffeomorphism operator. Not only to domains i

Traces of Besov and Triebel-Lizorkin spa
Traces of Besov and Triebel-Lizorkin spaces on domains
✍ Cornelia Schneider 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 258 KB

## Abstract We determine the trace of Besov spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathfrak {B}^s\_{p,q}(\Omega )$\end{document} and Triebel‐Lizorkin spaces \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathfrak {F}^s\_{p

Decomposition for Morrey type Besov–Trie
Decomposition for Morrey type Besov–Triebel spaces
✍ Henggeng Wang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 167 KB

## Abstract In this paper, the author establishes the decomposition of Morrey type Besov–Triebel spaces in terms of atoms and molecules concentrated on dyadic cubes, which have the same smoothness and cancellation properties as those of the classical Besov–Triebel spaces. The results extend those o

Real interpolations for Besov and Triebe
Real interpolations for Besov and Triebel-Lizorkin spaces on spaces of homogeneous type
✍ Dachun Yang 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 226 KB

## Abstract The author establishes a full real interpolation theorem for inhomogeneous Besov and Triebel‐Lizorkin spaces on spaces of homogeneous type. The corresponding theorem for homogeneous Besov and Triebel‐Lizorkin spaces is also presented. Moreover, as an application, the author gives the re