STABILITY AND MORREY SPACES RELATED TO MULTIPLIERS

Abstract

We apply wavelets to study the generalized local Morrey-Campanato spaces $M_{\phi, p}(\mathbb{R}^{n})$ and their preduals. As applications, we characterize the multipliers on $M_{\phi, p}(\mathbb{R}^{n})$ and the stability of these spaces under the perturbation of Calderón-Zygmund operators. Our results indicate that there exist some $M_{\phi, p}(\mathbb{R}^{n})$ without unconditional basis. This fact shows that $M_{\phi, p}(\mathbb{R}^{n})$ have some different characteristics unlike the classical Morrey spaces.