location:  Publications → journals → CJM
Abstract view

# Reverse Hypercontractivity for Subharmonic Functions

Published:2005-06-01
Printed: Jun 2005
• Leonard Gross
• Martin Grothaus
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

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 {\it 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: Reverse hypercontractivity, subharmonic
 MSC Classifications: 58J35 - Heat and other parabolic equation methods 47D03 - Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 47D07 - Markov semigroups and applications to diffusion processes {For Markov processes, see 60Jxx} 32Q99 - None of the above, but in this section 60J35 - Transition functions, generators and resolvents [See also 47D03, 47D07]