Molecular decomposition and Fourier multipliers for holomorphic Besov and Triebel–Lizorkin spaces

Abstract

Smooth molecular decompositions for holomorphic Besov and Triebel–Lizorkin spaces on the unit disk of the complex plane are constructed. The decompositions are used to obtain a boundedness result for Fourier multipliers. As further applications, we provide equivalent norms for the spaces under consideration, we consider the implications of the results on Hardy and Hardy–Sobolev spaces, and we study boundedness of coefficient multipliers.