Fourier multipliers for Hölder continuous functions and maximal regularity
Volume 160 / 2004
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.
