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

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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.
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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/

[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