On estimates for the Bessel transform
Abstract
Using a Bessel translation operator, we obtain a generalization of Theorem 2.2 in [3] for the Bessel transform for functions satisfying the (ψ,δ,β)-Bessel Lipschitz condition in the space L2,α(ℝ+).
Keywords
Bessel operator; Bessel transform; Bessel translation operator
References
2. Abilov V.A., Abilova F.V., Kerimov M.K., On estimates for the Fourier–Bessel Integral transform in the $L_2(\mathbb{R}_+)$, Comp. Math. Math. Phys. 49 (2009), no. 7, 1103–1110.
3. El Hamma M., Daher R., Generalization of Titchmarsh’s theorem for the Bessel transform, Rom. J. Math. Comput. Sci. 2 (2012), no. 2, 17–22.
4. Kipriyanov I.A., Singular Elliptic Boundary Value Problems, Nauka, Moscow, 1997 (in Russian).
5. Levitan B.M., Expansion in Fourier series and integrals over Bessel functions, Uspekhi Mat. Nauk 6 (1951), no. 2, 102–143.
6. Sveshnikov A.G., Bogolyubov A.N., Kravtsov V.V., Lectures on Mathematical Physics, Nauka, Moscow, 2004 (in Russian).
7. Titchmarsh E.C., Introduction to the Theory of Fourier Integrals, Claredon, Oxford, 1948; Komkniga, Moscow, 2005.
8. Trimèche K., Transmutation operators and mean-periodic functions associated with differential operators, Math. Rep. 4 (1988), no. 1, 1–282.
9. Watson G.N., Treatise on the Theory of Bessel Functions, Inostrannaya Literatura, Moscow, 1949; Cambridge University Press, Cambridge, 1952.
10. Zayed A.L., Handbook of Function and Generalized Function Transformations, CRC, Boca Raton, 1996.
Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Morocco Morocco
Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Morocco Morocco
Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, Morocco Morocco
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
- License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license. - Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s. - User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor. - Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
