Geodesic
Fourier multipliers for Hölder continuous functions and maximal regularity
Wolfgang Arendt1 ; Charles Batty2 ; Shangquan Bu3
1Abteilung Angewandte Analysis Universität Ulm 89069 Ulm, Germany
2St. John's College University of Oxford Oxford OX1 3JP, Great Britain
3Department of Mathematical Science University of Tsinghua 100084 Beijing, China and Abteilung Angewandte Analysis Universität Ulm 89069 Ulm, Germany
Studia Mathematica, Tome 160 (2004) no. 1, pp. 23-51
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm160-1-2
Keywords: operator valued fourier multiplier theorems lder spaces proved periodic other line contrast p situation arbitrary banach spaces consequence maximal regularity sense lder characterized simple resolvent estimates underlying operator

Wolfgang Arendt  1   ; Charles Batty  2   ; Shangquan Bu  3

1 Abteilung Angewandte Analysis Universität Ulm 89069 Ulm, Germany
2 St. John's College University of Oxford Oxford OX1 3JP, Great Britain
3 Department of Mathematical Science University of Tsinghua 100084 Beijing, China and Abteilung Angewandte Analysis Universität Ulm 89069 Ulm, Germany 
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 and maximal regularity
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Wolfgang Arendt; Charles Batty; Shangquan Bu. Fourier multipliers for Hölder continuous functions
 and maximal regularity. Studia Mathematica, Tome 160 (2004) no. 1, pp. 23-51. doi: 10.4064/sm160-1-2

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