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In this paper we give sufficient conditions on a measurable function p : (0, ∞) n → [1, ∞) 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(•) ((0, ∞) n , µα), where dµα(x) = 2 n n j=1 x 2α j +1 j e −x 2 j Γ(α j +1) dx, being α = (α 1 , . . . , αn) ∈ [0, ∞) n and x = (x 1 , . . . , xn) ∈ (0, ∞) n .

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