The compactly supported wavelet characterization of non-homogeneous Herz-Sobolev spaces with variable exponent

摘要

Our aim in the present paper is to introduce non-homogeneous Herz-Sobolev spaces with variable exponent and to obtain a wavelet characterization and an unconditional basis of them using wavelets with proper decay and compact support. Our method is based on the extrapolation theorem and duality argument.