On $L^p$-contractivity of Laguerre semigroups

TL;DR

This paper investigates the conditions under which various Laguerre and Bessel semigroups are contractive across all L^p spaces, providing sharp parameter ranges and extending understanding of these operators' behaviors.

Contribution

It determines the precise parameter ranges for L^p-contractivity of Laguerre semigroups and explores similar properties for related Bessel semigroups, offering new insights.

Findings

Identified sharp parameter ranges for Laguerre semigroup contractivity

Extended analysis to Bessel semigroups with similar contractivity properties

Provided comprehensive conditions for L^p stability of these 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.