Harmonic analysis operators related to symmetrized Jacobi expansions

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.