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

Abstract

In this paper we give sufficient conditions on a measurable function $p:(0,\infty {)}^n\to [1,\infty )$ 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 $x=(x_1,\dots ,x_n)\in (0,\infty {)}^n$.

34 pages