Dual ultracontractivity and its applications

Abstract

The ultracontractivity is well studied and several equivalent conditions are known. In this paper, we introduce the dual notion of the ultracontractivity, which we call the dual ultracontractivity. We give necessary and sufficient conditions for the dual ultracontractivity. As an application, we discuss one-dimensional diffusion processes. We can write the conditions for the dual ultracontractivity in terms of speed measures.

Keywords

Dual ultracontractivity / one-dimensional diffusion processes / Nash inequality / interpolation

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Higher Education Press and Springer-Verlag Berlin Heidelberg