On Kato-Sobolev type spaces

TL;DR

This paper investigates Kato-Sobolev type spaces, establishing their properties, a Wiener-Levy theorem, and analyzing Schatten-von Neumann characteristics of associated pseudo-differential operators.

Contribution

It introduces and studies properties of the spaces ${\

Findings

Proves a weak Wiener-Levy theorem for these spaces.

Establishes Schatten-von Neumann properties of pseudo-differential operators with symbols in these spaces.

Provides an integral representation formula based on Calderón's techniques.

Abstract

We study an increasing family of spaces ${\mathcal{B}_{k}^{p}}_{1\leq p\leq \infty}$ 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}%_{k}^{p} $ spaces.