Endpoint estimates for harmonic analysis operators associated with Laguerre polynomial expansions

Abstract

In this paper we give a criterion to prove boundedness results for several operators from H1 ((0, ∞), γα) to L 1 ((0, ∞), γα) and also from L∞((0, ∞), γα) to BMO((0, ∞), γα), with respect to the probability measure dγα(x) = 2 Γ(α+1) x 2α+1e −x 2 dx on (0, ∞) when α > − 1 2 . We shall apply it to establish endpoint estimates for Riesz transforms, maximal operators, Littlewood-Paley functions, multipliers of Laplace transform type, fractional integrals and variation operators in the Laguerre setting.