Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 4: 899 - 928

DOI: https://doi.org/10.1007/s11464-014-0398-y

RESEARCH ARTICLE

Dual ultracontractivity and its applications

  • Ichiro SHIGEKAWA
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  • Department of Mathematics, Kyoto University, Kyoto 606-8502, Japan

Received date: 04 Apr 2014

Accepted date: 01 May 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Dual ultracontractivity; one-dimensional diffusion processes; Nash inequality; interpolation

Cite this article

Ichiro SHIGEKAWA . Dual ultracontractivity and its applications[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 899 -928 . DOI: 10.1007/s11464-014-0398-y

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