OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES

Abstract

Abstract:

The authors establish operator-valued Fourier multiplier theorems on Triebel
spaces on RN, where the required smoothness of the multiplier functions depends on the
dimension N and the indices of the Triebel spaces. This is used to give a sufficient condition
of the maximal regularity in the sense of Triebel spaces for vector-valued Cauchy problems
with Dirichlet boundary conditions.

Key words: Operator-valued Fourier multiplier, vector-valued Triebel space, Fourier
type, vector-valued maximal inequality, maximal regularity

CLC Number:

42A75

Kim Jin-Myong, BU Chang-Quan. OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES[J].Acta mathematica scientia,Series B, 2005, 25(4): 599-609.

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