Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in R²
Two operator-valued Fourier multiplier theorems for Hölder spaces are proved, one periodic, the other on the line. In contrast to the -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.
We investigate the relation between the rate of decrease of a Fourier transform and the possible algebraic relations on its support.