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Operator‐Valued Fourier Multipliers, Vector ‐ Valued Besov Spaces, and Applications
Author(s) -
Amann Herbert
Publication year - 1997
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.3211860102
Subject(s) - mathematics , differential operator , invariant (physics) , complement (music) , fourier transform , mathematical analysis , operator (biology) , pure mathematics , elliptic operator , multiplier (economics) , biochemistry , chemistry , macroeconomics , repressor , complementation , transcription factor , economics , mathematical physics , gene , phenotype
It is shown that translation‐invariant operation, with operator‐valued symbols act continuously on Bcsov spaces of Band‐space‐valued distributions. This result is then used to extend and complement the known theory of vector‐valued Bcsov spaces. In addition, its power is demonstrated by giving applications to a variety of problems from elliptic and parabolic differential and integro‐differential equations.