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We investigate some multiplication properties of Kato-Sobolev spaces byadapting the techniques used in the study of Beurling algebras by Coifman andMeyer. Also we develop an analytic functional calculus for Kato-Sobolevalgebras based on an integral representation formula belonging A. P.Calder\'{o}n.

On Kato-Sobolev spaces. The Wiener-L\'{e}vy theorem for Kato-Sobolev algebras $\mathcal{H}_{\mathtt{ul}}^{s}$