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arXiv · 2202.11137

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

Jorge J. Betancor·Estefanía Dalmasso·Pablo Quijano·Roberto Scotto
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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 $α$-Laguerre polynomial expansions are bounded on the variable Lebesgue space $L^{p(\cdot)} ((0,\infty)^n, μ_α)$, where $dμ_α(x)=2^n\prod_{j=1}^n \frac{x_j^{2α_j+1} e^{-x_j^2}}{Γ(α_j+1)} dx$, being $α=(α_1, \dots, α_n)\in [0,\infty)^n$ and $x=(x_1,\dots,x_n)\in (0,\infty)^n$.

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Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto. 2022-02-22. Harmonic analysis operators associated with Laguerre polynomial expansions on variable Lebesgue spaces. https://arxiv.org/abs/2202.11137

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