Hölder’s inequality for perturbations of positive semigroups by potentials

The objective of this note is to give an estimate for a positive perturbed semigroup in terms of the free one. Here we consider perturbation by a potential and the estimate is given by a pointwise Hölder inequality. As a consequence it is shown that ultracontractivity and Gaussian upper bounds are preserved by such perturbations.  2005 Elsevier Inc. All rights reserved