On Kato-Sobolev type spaces

Abstract: We study an increasing family of spaces $${\mathcal{B}<em>{k}^{p}}</em>{1\leq p\leq \infty}$$ by adapting the techniques used in the study of Beurling algebras by Coifman and Meyer (1978). A weak form Wiener-Levy theorem is proved based on an integral representation formula belonging A. P. Calder\'{o}n. Also we study the Schatten-von Neumann properties of pseudo-differential operators with symbols in the spaces $\mathcal{B}$ spaces.