Variation inequalities for Riesz transforms and Poisson semigroups associated with Laguerre polynomial expansions

TL;DR

This paper proves $L^p$-boundedness for variation, oscillation, and jump operators linked to Riesz transforms and Poisson semigroups in the context of Laguerre polynomial expansions, advancing harmonic analysis techniques.

Contribution

It introduces new $L^p$-boundedness results for these operators specifically for Laguerre polynomial expansions, expanding the understanding of harmonic analysis in this setting.

Findings

Established $L^p$-boundedness for variation operators

Proved boundedness for oscillation and jump operators

Applied results to Riesz transforms and Poisson semigroups

Abstract

In this paper we establish $L^p$-boundedness properties for variation, oscillation and jump operators associated with Riesz transforms and Poisson semigroups related to Laguerre polynomial expansions.