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Fourier multipliers for Hölder continuous functions and maximal regularity

Wolfgang Arendt, Charles Batty, Shangquan Bu (2004)

Studia Mathematica

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.

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