Harmonic analysis operators associated with Laguerre polynomial expansions on variable Lebesgue spaces

TL;DR

This paper establishes conditions under which harmonic analysis operators related to Laguerre polynomial expansions are bounded on variable Lebesgue spaces, extending classical results to a more flexible functional setting.

Contribution

It provides new sufficient conditions for the boundedness of harmonic analysis operators associated with Laguerre expansions on variable Lebesgue spaces.

Findings

Boundedness of maximal operators on variable Lebesgue spaces

Boundedness of Riesz transforms in the variable setting

Boundedness of Littlewood--Paley functions and multipliers

Abstract

In this paper we give sufficient conditions on a measurable function $p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysis operators (maximal operators, Riesz transforms, Littlewood--Paley functions and multipliers) associated with $\alpha$-Laguerre polynomial expansions are bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n, \mu_\alpha)$, where $d\mu_\alpha (x)=2^n\prod_{j=1}^n \frac{x_j^{2\alpha_j+1} e^{-x_j^2}}{\Gamma(\alpha_j+1)} dx$, being $\alpha=(\alpha_1, \dots, \alpha_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$.