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

摘要

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