A Transference Result of the Lp-Continuity of the Jacobi Littlewood-Paley g-Function to the Gaussian and Laguerre Littlewood-Paley g-Function

Abstract

We develop a transference method to obtain the Lp-continuity of the Gaussian-Littlewood-Paley g-function and the Lp-continuity of the Laguerre-Littlewood-Paley g-function from the Lp-continuity of the Jacobi-Littlewood-Paley g-function, in dimension one, using the well-known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials.