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 $H^1((0,\infty ),{\gamma }_{\alpha })$ to $L^1((0,\infty ),{\gamma }_{\alpha })$ and also from $L^{\infty }((0,\infty ),{\gamma }_{\alpha })$ to $\BMO((0,\infty),γ_α)$, with respect to the probability measure $d{\gamma }_{\alpha }(x)=\frac{2}{\Gamma (\alpha +1)}{x}^{2\alpha +1}{e}^{-x^2}dx$ on $(0,\infty )$ when $\alpha >-\frac{1}{2}$. 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.

22 pages