  We investigate some multiplication properties of Kato-Sobolev spaces by
adapting the techniques used in the study of Beurling algebras by Coifman and
Meyer. We develop an analytic functional calculus for Kato-Sobolev algebras
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 Kato-Sobolev spaces.
