数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (4): 599-609.

• 论文 • 上一篇    下一篇

OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES

Kim Jin-Myong,步尚全   

  1. Department of Mathematical Science, University of Tsinghua, Beijing 100084, China

    Department of Mathematics, University of Kim Il Sung, DPR Korea
    Department of Mathematical Science, University of Tsinghua, Beijing 100084, China  
  • 出版日期:2005-10-11 发布日期:2005-10-11
  • 基金资助:

    The first author is supported by the NSF of China (A01010703), the Specialized
    Research Fund for the Doctoral Program of Higher Education and the Excellent Young Teacher Program
    of MOE,P.R.C.

OPERATOR-VALUED FOURIER MULTIPLIER THEOREMS ON TRIEBEL SPACES

 Kim Jin-Myong, BU Chang-Quan   

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    The first author is supported by the NSF of China (A01010703), the Specialized
    Research Fund for the Doctoral Program of Higher Education and the Excellent Young Teacher Program
    of MOE,P.R.C.

摘要:

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.

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

中图分类号: 

  • 42A75