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In this paper we give sufficient conditions on a measurable function$p:(0,\infty)^n\rightarrow [1,\infty)$ in order that harmonic analysisoperators (maximal operators, Riesz transforms, Littlewood--Paley functions andmultipliers) associated with $\alpha$-Laguerre polynomial expansions arebounded 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 $x=(x_1,\dots,x_n)\in (0,\infty)^n$.

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