OPERATOR-VALUED FOURIER MULTIPLIERS, VECTOR-VALUED BESOV-SPACES, AND APPLICATIONS

Authors
AMANN H
Citation
H. Amann, OPERATOR-VALUED FOURIER MULTIPLIERS, VECTOR-VALUED BESOV-SPACES, AND APPLICATIONS, Mathematische Nachrichten, 186, 1997, pp. 5-56
Citations number
55
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Mathematische Nachrichten → ACNP
ISSN journal
0025584X
Volume
186
Year of publication
1997
Pages
5 - 56
Database
ISI
SICI code
0025-584X(1997)186:<5:OFMVBA>2.0.ZU;2-V
Abstract
It is shown that translation-invariant operators with operator-valued symbols act continuously on Besov spaces of Banach-space-valued distri butions. This result is then used to extend and complement the known t heory of vector- valued Besov spaces. In addition, its power is demons trated by giving applications to a variety of problems from elliptic a nd parabolic differential and integrodifferential equations.