Decompositions and Characterizations of Besov-Hausdorff and Triebel-Lizorkin Spaces with Variable Smoothness and Integerability

Abstract

We show the decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces. We also show the characterizations of Besov-Lipschitz, Besov-Morrey and Triebel-Lizorkin-Morrey spaces by maximal functions, local mean and including 𝒬 spaces. The function spaces, Besov-type spaces and atomic decomposition with variable smoothness and integrability are studied.