$L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators

TL;DR

This paper establishes weak type (1,1) bounds for maximal operators linked to heat semigroups of Bessel and Laguerre operators, simplifying previous proofs and extending known results.

Contribution

It provides a unified, simpler proof of weak type (1,1) bounds for maximal operators associated with Bessel and Laguerre semigroups, including known results as special cases.

Findings

Maximal operators are weak type (1,1) for Bessel and Laguerre semigroups.

Results include and extend previous known bounds.

Proofs are simpler than existing methods.

Abstract

In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler than the ones for the known special cases.