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, ∞) 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 Lp(·) ((0, ∞) n, µα), where dµα(x) = 2n Qn j=1 x 2αj+1 j e −x 2 j Γ(αj+1) dx, being α = (α1, . . . , αn) ∈ [0,∞) n and x = (x1, . . . , xn) ∈ (0, ∞) n.