Calderón's formulas and uncertainty principles for the Laguerre–Bessel L α 2 -multiplier operators

Abstract

The main purpose of this paper is to introduce the Laguerre–Bessel L α 2 -multiplier operators and to give some results related to these operators as Plancherel's, Calderón's reproducing formulas and Heisenberg's, Donoho–Stark's uncertainty principles. Next, using the theory of reproducing kernels we give best estimates and an integral representation of the extremal functions related to this operators.