A transference result of the L^p continuity of the Jacobi Littlewood-Paley g-function to the Gaussian and Laguerre Littlewood-Paley g-function

TL;DR

This paper establishes a transference principle that extends the L^p continuity properties of the Jacobi Littlewood-Paley g-function to analogous functions in Gaussian and Laguerre settings, broadening the scope of harmonic analysis tools.

Contribution

It introduces a novel transference method that connects Jacobi, Gaussian, and Laguerre Littlewood-Paley g-functions, enabling the transfer of L^p continuity results across these contexts.

Findings

L^p continuity of Jacobi Littlewood-Paley g-function established

Transference of L^p bounds to Gaussian and Laguerre cases achieved

Framework enhances harmonic analysis techniques across different orthogonal systems

Abstract

A transference result of the L^p continuity of the Jacobi Littlewood-Paley g-function to the Gaussian and Laguerre Littlewood-Paley g-function.