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Atomic decomposition for weighted Besov and Triebel‐Lizorkin spaces
Author(s) -
Izuki Mitsuo,
Sawano Yoshihiro
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910201
Subject(s) - mathematics , class (philosophy) , besov space , pure mathematics , decomposition , function space , function (biology) , weight function , key (lock) , interpolation space , mathematical analysis , functional analysis , computer science , artificial intelligence , ecology , biochemistry , chemistry , evolutionary biology , biology , gene , computer security
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.