Title: On estimates for the first Hankel-Clifford transform
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-21-00029; Volume 4 / Issue 1 / Year 2022, Pages 23-30
Document Type: Research Paper
Author(s): Mohamed El Hamma a , Radouan Daher b , Hasnaa Lahmadi c
aUniversité Hassan II, Faculté des Sciences Aïn Chock, Département de mathématiques et informatique, Laboratoire Topologie, Algèbre, Géométrie et Mathématiques Discrètes, Casablanca, Maroc
bUniversité Hassan II, Faculté des Sciences Aïn Chock, Département de mathématiques et informatique, Laboratoire Topologie, Algèbre, Géométrie et Mathématiques Discrètes, Casablanca, Maroc
cUniversité Hassan II, Faculté des Sciences Aïn Chock, Département de mathématiques et informatique, Laboratoire Topologie, Algèbre, Géométrie et Mathématiques Discrètes, Casablanca, Maroc
Received: 27 April 2021, Accepted: 28 August 2021, Published: 18 September 2021.
Corresponding Author: Mohamed El Hamma (Email address: m_elhamma@yahoo.fr)
Full Text: PDF
Abstract
In this work, we obtain new inequalities for the first Hankel-Clifford transform in the space L2((0, +∞), xμ), μ ≥ 0, using a generalized translation operator for proving these estimates in certain classes of functions characterized by a generalized continuity modulus.
Keywords: First Hankel-Clifford transform, generalized translation operator
References:- V. A. Abilov and F. V. Abilova and M. K. Kerimov, Some Remarks concerning the Fourier transform in the space L2(ℝ), Comp. Math. Math. Phys. 48 (6), 885–891, 2008.
- V. A. Abilov and F. V. Abilova and M. K. Kerimov, On Estimates for the Fourier-Bessel integral in the space L2(ℝ+), Comp. Math. Math. Phys. 49 (7), 1103–1110, 2009.
- V. A. Abilov and F. V. Abilova, Approximation of Functions by Fourier-Bessel sums, IZV. Vyssh. Uchebn Zaved. Mat. 45 (8), 3–9, 2001.
- J. J. Betancor, The Hankel-Clifford transformation on certain spaces of ultradistributions, Indian. J. Pure Appl. Math. 20 (6), 583–603, 1989.
- R. Daher and M. El Hamma, Some estimates for the Jacobi transform in the space L2(ℝ+, Δ(α, β)(t)dt), Int. J. Applied Math. 25 (1), 13–23, 2012.
- M. El Hamma, R. Daher and A. Khadari, On estimates for the Dunkl transform in the space L2(ℝ2, wk(x)dx), FACTA UNIVERSITATIS (NIS). Ser. Math. Inform 28 (3) 285–296, 2013.
- A. Gray, G. B. Matthews and T. M. Macrobert, A treatise on Bessel functions and their applications to physics, MacMillan, London, 1952.
- D. T. Haimo, Integral equations associated with Hankel convolution, Trans. Amer. Math. Soc. 116, 1965.
- B. M. Levitan, Expansion in Fourier series and integrals over Bessel functions, Uspekhi Math.Nauk, 6 (2), 102–143, 1951.
- J. M. R. Méndez Pérez and M. M. Socas Robayna, A pair of generalized Hankel-Clifford transformation and their applications, J. Math. Anal. Appl. 154 543–557, 1991.
- S. M. Nikol’skii, Approximation of functions of Several variables and Embedding theorems, Nauka, Moscow, 1996. (in Russian).
- P. Prasad and V. K. Singh Pseudo-differential operators involving Hankel-Clifford transformations, Asian-European. J. Math. 5 (3), 2012, (15 pages).
- P. Prasad and V. K. Singh Pseudo-differential operators associated to a pair of Hankel-Clifford transformations on certain Beurling type function spaces, Asian-European. J. Math. 6 (3), 2013, (22 pages).
- A. H. Zemanian, Generalized integral transformations, Interscience Publishers, New York, 1968.