Transference of Lp bounds between symmetrized Jacobi expansions and Dunkl transform

Abstract

We prove two theorems showing connections between multipliers for the symmetrized Jacobi expansions and multipliers for the Dunkl transform on $$\mathbb{R}$$ . These results can be seen as generalizations of the classical Igari’s result relating Jacobi and Hankel multipliers. Moreover, we show a transference theorem relating Jacobi and Dunkl transplantations.