Harmonic analysis operators related to symmetrized Jacobi expansions

TL;DR

This paper studies harmonic analysis operators related to symmetrized Jacobi expansions, exploring their properties and extending results to classical Jacobi expansions, advancing understanding of these mathematical structures.

Contribution

It introduces a symmetrization approach for Jacobi expansions and analyzes key harmonic analysis operators within this framework, providing new insights and results.

Findings

Mapping properties of Riesz transforms established

Boundedness of Poisson semigroup maximal operator demonstrated

New results obtained for classical Jacobi expansions

Abstract

Following a symmetrization procedure proposed recently by Nowak and Stempak, we consider the setting of symmetrized Jacobi expansions. In this framework we investigate mapping properties of several fundamental harmonic analysis operators, including Riesz transforms, Poisson semigroup maximal operator, Littlewood-Paley-Stein square functions and multipliers of Laplace and Laplace-Stieltjes transform type. Our paper delivers also some new results in the original setting of classical Jacobi expansions.