ON ESTIMATES FOR THE CANONICAL LINEAR FOURIER-BESSEL TRANSFORM IN THE SPACE Lp (R+; x2+1dx) (1 < p 2)

Akhlidj Abdellatif, Zakaria Sadiq

DOI Number
https://doi.org/10.22190/FUMI220912033A
First page
509
Last page
517

Abstract


In this paper, we establish the analog of Abilov's theorems and the analog of Titchmarsh's theorems for the canonical linear Fourier-Bessel transform in a class of functions in the space $L^{p}(\mathbb{R}^{+},x^{2\alpha+1}dx)$ where $1<p\leq2$ and $\alpha>\frac{-1}{2}$. The proof of the theorems are based on the algebraic properties associated with the canonical linear Fourier-Bessel transform.

Keywords

Canonical linear Fourier-Bessel operator, Canonical linear Fourier-Bessel Transform, Translation operators associated with the canonical linear Fourier-Bessel operator, Generalized modulus of continuity.

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References


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DOI: https://doi.org/10.22190/FUMI220912033A

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