Fraction powers of a class of mellin multiplier transforms part ii

Abstract

In a previous paper we developed a theory of fractional powers for a class of Mellin multiplier transforms within the framework of weighted L spaces. In the present paper, we extend these ideas to a wider class of operators acting on certain spaces of testing-functions. Fractional powers can be defined and index laws established under conditions of great generality. Results involving adjoints are stated in preparation for a distributional treatment in a subsequent paper