On $L^{p}$-contractivity of Laguerre semigroups

Abstract

We study several Laguerre semigroups appearing in the literature and find sharp ranges of type parameters for which these semigroups are contractive on all $L^{p}$ spaces, $1\le p\le\infty$. We also answer a similar question for Bessel semigroups, which in a sense are closely related to the Laguerre semigroups. A bit surprisingly, in some cases the ranges turn out to be disconnected sets.