Uncertainty principles and Calderón's formulas for the deformed Hankel $L^2_\alpha$-multiplier operators

A. Chana, A. Akhlidj

Laboratory of Fundamental and Applied Mathematics, Department of Mathematics and Informatics, Faculty of Sciences Ain Chock, University of Hassan II, B.P 5366 Maarif, Casablanca, Morocco

Аннотация: The main purpose of this paper is to introduce the deformed Hankel $L^2_\alpha$-multiplier operators and to 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.

Ключевые слова: deformed Hankel transform, Calderón's reproducing formulas, extremal functions, Heisenberg's uncertainty principle, Donoho-Stark's uncertainty principle.

УДК: 517.44, 517.983

MSC: 42B10, 47G30, 47B10

Поступила в редакцию: 22.06.2024
Исправленный вариант: 25.09.2024
Принята в печать: 09.09.2024

Язык публикации: английский

DOI: 10.15393/j3.art.2024.16330