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Fourier multipliers for Hölder continuous functions and maximal regularity

Volume 160 / 2004

Wolfgang Arendt, Charles Batty, Shangquan Bu Studia Mathematica 160 (2004), 23-51 MSC: Primary 42A45; Secondary 34G10, 47D06. DOI: 10.4064/sm160-1-2

Abstract

Two operator-valued Fourier multiplier theorems for Hölder spaces are proved, one periodic, the other on the line. In contrast to the $L^p$-situation they hold for arbitrary Banach spaces. As a consequence, maximal regularity in the sense of Hölder can be characterized by simple resolvent estimates of the underlying operator.

Authors

  • Wolfgang ArendtAbteilung Angewandte Analysis
    Universität Ulm
    89069 Ulm, Germany
    e-mail
  • Charles BattySt. John's College
    University of Oxford
    Oxford OX1 3JP, Great Britain
    e-mail
  • Shangquan BuDepartment of Mathematical Science
    University of Tsinghua
    100084 Beijing, China
    and
    Abteilung Angewandte Analysis
    Universität Ulm
    89069 Ulm, Germany
    e-mail

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