Derivative and Lipschitz Type Characterizations of Variable Exponent Bergman Spaces

Abstract

We give derivative and Lipschitz type characterizations of Bergman spaces with log-Hölder continuous variable exponent.

Atomic Decomposition and Composition Operators on Variable Exponent Bergman Spaces

“…Then in [3] and [4], the authors characterized Toeplitz operators and Carleson measures for variable exponent Bergman spaces, which are generalizations of constant exponent Bergman spaces. In [11], some derivative and Lipschitz type characterizations of variable exponent Bergman spaces in several variables were obtained by Ma and Xu. And in [8], Ferguson investigated the question when two weighted variable exponent Bergman spaces or Hardy spaces are equivalent and proved an analogue of Littlewood subordination and a result on the boundedness of composition operators when the exponent p(•) is harmonic and log-Hölder continuous with bounded conjugate.…”