Uncertainty Principles and Extremal Functions for Bessel Multiplier Operators in Quantum Calculus

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Ahmed Chana
Abdellatif Akhlidj

Abstract

Using the q-Jackson integral and some elements of the q-harmonic analysis associated with the q-Bessel operator for fixed 0 < q < 1, we introduce the q-Bessel multiplier operators and we give some new 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 these operators on weighted Sobolev spaces.

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