Lp-Lq estimates for transition semigroups associated to dissipative stochastic systems

In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroup associated with a stochastic partial differential equation. This is done in terms of exponential integrability of Lipschitz functions and some logarithmic Sobolev-type inequalities with respect to invariant measures. The abstract characterization results concerning the improvement of summability can be applied to transition semigroups associated to stochastic reaction-diffusion equations. (c) 2025 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).