Decay of Fourier Transforms and Generalized Besov Spaces

Abstract

A characterization of the generalized Lipschitz and Besov spaces in terms of decay of Fourier transforms is given. In particular, necessary and sufficient conditions of Titchmarsh type are obtained. The method is basedon two-sided estimate for the rate of approximation of a β-admissible family of multipliers operators in terms of decayproperties of Fourier transforms.