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 Reverse hypercontractivity, subharmonic

MSC Classifications:

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

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