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Besov‐Morrey spaces and Triebel‐Lizorkin‐Morrey spaces on domains
Author(s) -
Sawano Yoshihiro
Publication year - 2010
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.200710151
Subject(s) - mathematics , pointwise , pure mathematics , multiplier (economics) , trace (psycholinguistics) , function space , operator (biology) , mathematical analysis , extension (predicate logic) , besov space , space (punctuation) , interpolation space , functional analysis , computer science , linguistics , philosophy , biochemistry , chemistry , repressor , gene , transcription factor , economics , macroeconomics , programming language , operating system
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 in R n we extend our definition of function spaces to compact oriented Riemannian manifolds. Among the properties above, the result for the trace operator is in particular interesting, which reflects the property of the parameters p , q in the Morrey space ℳ p q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)