Maximal Banach algebra in spaces of multipliers between Bessel potential spaces

Abstract

It is shown that the maximal Banach algebra $A_{p}^{{m,l}}$ imbedded in the space of multipliers between Bessel potential spaces $M(H_{p}^{m}({{R}^{n}}) \to H_{p}^{l}({{R}^{n}}))$ is isomorphic to $M(H_{p}^{m}({{R}^{n}}) \to H_{p}^{l}({{R}^{n}})) \cap {{L}_{\infty }}({{R}^{n}})$. A precise description of all imbeddings $A_{p}^{{m,l}} \subset A_{p}^{{\mu ,\lambda }}$ is given.