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Reverse Hypercontractivity for Subharmonic Functions
Published online by Cambridge University Press: 20 November 2018
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 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.
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- Copyright © Canadian Mathematical Society 2005
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