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Reverse Hypercontractivity for Subharmonic Functions

Published online by Cambridge University Press:  20 November 2018

Leonard Gross  and
Martin Grothaus
Leonard Gross
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853, U.S.A., e-mail: gross@math.cornell.edu
Martin Grothaus
Affiliation:
Fachbereich Mathematik, Universität Kaiserslautern, 67663 Kaiserslautern, Germany, e-mail: grothaus@mathematik.uni-kl.de
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Abstract

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Contractivity and hypercontractivity properties of semigroups are now well understood when the generator, $A$ , is a Dirichlet form operator. It has been shown that in some holomorphic function spaces the semigroup operators, ${{e}^{-tA}}$ , can be bounded below from ${{L}^{p}}$ to ${{L}^{q}}$ when $p,\,q$ and $t$ are suitably related. We will show that such lower boundedness occurs also in spaces of subharmonic functions.

Keywords

58J3547D0347D0732Q9960J35Reverse hypercontractivitysubharmonic

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 3 , 01 June 2005 , pp. 506 - 534
Copyright
Copyright © Canadian Mathematical Society 2005

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