Geodesic
Estimates for the second Hankel–Clifford transform and Titchmarsh equivalence theorem
Problemy analiza, Tome 13 (2024) no. 2, pp. 144-154

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain estimates of integrals containing the second Hankel–Clifford transforms of functions from Sobolev-Hankel–Clifford spaces. As a corollary, we obtain a new variant of Titchmarsh equivalence theorem for the second Hankel–Clifford transform.
Keywords: second Hankel–Clifford transform, Hankel–Clifford translation, Sobolev–Hankel–Clifford spaces, Titchmarsh equivalence theorem. 
S. S. Volosivets. Estimates for the second Hankel–Clifford transform and Titchmarsh equivalence theorem. Problemy analiza, Tome 13 (2024) no. 2, pp. 144-154. http://geodesic.mathdoc.fr/item/PA_2024_13_2_a7/
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[1] Bary N. K., Stechkin S. B., “Best approximation and differential properties of two conjugate functions”, Trudy Mosk. Mat. Obs., 5, 1956, 483–522 (in Russian) | MR | Zbl

[2] Bergh J., Löfström J., Interpolation spaces. An introduction, Springer-Verlag, Berlin-Heidelberg, 1976 | MR | Zbl

[3] Butzer P. L., Nessel R. J., Fourier analysis and approximation, Birkhauser, Basel-Stuttgart, 1971 | Zbl

[4] El Hamma M., Daher R., Mahfoud A., “An analogue of Titchmarsh theorem for the first Hankel–Clifford transform”, J. Anal., 29:4 (2021), 1129–1136 | DOI | MR | Zbl

[5] Gray A., Matthecos G. B., MacRobert T. M., A treatise on Bessel functions and their applications to physics, Macmillan, London, 1952 | MR

[6] Hayek N., “Sobre la transformacion de Hankel”, Actas de la VIII Reunion Anual de Matematicos Epanoles, 1967, 47–60

[7] Lahmadi H., El Hamma M., “On estimates for the Hankel–Clifford transform in the space $L^p_\mu$”, J. Anal., 31:2 (2023), 1479–1486 | DOI | MR | Zbl

[8] Lorentz G. G., “Fourier–Koeffizienten und Funktionenklassen”, Math. Zeitchr., 51:3 (1948), 135–149 | DOI | MR | Zbl

[9] Méndez Pérez J. M. R., Socas Robayna M. M., “A pair of generalized Hankel–Clifford transformation and their applications”, J. Math. Anal. Appl., 154:2 (1991), 543–557 | DOI | MR | Zbl

[10] Platonov S. S., “Generalized Bessel translations and some problems of aprroximation of functions theory in metric $L_2$. II”, Proc. Petrozavodsk State Univ. Matematika, 8 (2001), 20–36 (in Russian) | MR | Zbl

[11] Platonov S. S., “Bessel harmonic analysis and approximation of functions on the half-line”, Izv Math., 71:5 (2007), 1001–1048 | DOI | MR | Zbl

[12] Prasad A., Singh V. K., Dixit M. M., “Pseudo-differential operators involving Hankel–Clifford transformations”, Asian-European. J. Math., 5:3 (2012), 1250040, 15 pp. | DOI | MR | Zbl

[13] Prasad A., Singh V. K., “Pseudo-differential operators associated to a pair of Hankel–Clifford transformations on certain Beurling type function spaces”, Asian-European J. Math., 6:3 (2013), 1350039, 22 pp. | DOI | MR | Zbl

[14] Titchmarsh E., Introduction to the theory of Fourier integrals, Clarendon press, Oxford, 1937 | MR | Zbl

[15] Volosivets S. S., “Weighted integrability results for first Hankel–Clifford transform”, Prob. Anal. Issues Anal., 12(30):2 (2023), 107–117 | DOI | MR

[16] Volosivets S. S., “Dual Boas-type theorems and weighted integrability results for second Hankel–Clifford transform”, J. Pseudo-Differ. Oper. Appl., 14 (2023), 48 | DOI | MR | Zbl

[17] Volosivets S. S., “Fourier–Bessel transforms from generalized Lipschitz spaces and weighted Lebesgue spaces”, Ann. Univ. Ferrara Ser. VII Sci. Mat., 70:2 (2024), 285–306 | DOI | MR