Geodesic
Weighted integrability results for first Hankel-Clifford transform
Problemy analiza, Tome 12 (2023) no. 2, pp. 107-117.

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

We obtain sufficient conditions for the weighted integrability of the first Hankel-Clifford transforms of functions from generalized integral Lipschitz classes. These conditions are analogues and generalization of well-known Titchmarsh conditions for the classical Fourier transform.
Keywords: first Hankel-Clifford transform, Hankel-Clifford translation, generalized Lipschitz spaces, weighted integrability. 
@article{PA_2023_12_2_a7,
     author = {S. S. Volosivets},
     title = {Weighted integrability results for first {Hankel-Clifford} transform},
     journal = {Problemy analiza},
     pages = {107--117},
     publisher = {mathdoc},
     volume = {12},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2023_12_2_a7/}
}
TY  - JOUR
AU  - S. S. Volosivets
TI  - Weighted integrability results for first Hankel-Clifford transform
JO  - Problemy analiza
PY  - 2023
SP  - 107
EP  - 117
VL  - 12
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2023_12_2_a7/
LA  - en
ID  - PA_2023_12_2_a7
ER  - 
%0 Journal Article
%A S. S. Volosivets
%T Weighted integrability results for first Hankel-Clifford transform
%J Problemy analiza
%D 2023
%P 107-117
%V 12
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2023_12_2_a7/
%G en
%F PA_2023_12_2_a7
S. S. Volosivets. Weighted integrability results for first Hankel-Clifford transform. Problemy analiza, Tome 12 (2023) no. 2, pp. 107-117. http://geodesic.mathdoc.fr/item/PA_2023_12_2_a7/

[1] Abilov V. A., Abilova F. V., “Approximation of functions by Fourier-Bessel sums”, Russian Math. (Izv. VUZ. Matem.), 45:8 (2001), 1–7 | 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] Daher R., Tyr O., “Integrability of the Fourier-Jacobi transform of functions satisfying Lipschitz and Dini-Lipschitz-type estimates”, Integral Transforms Spec. Funct., 2022 (to appear) | DOI | MR

[5] El Hamma M., Mahfoud A., “Generalization of Titchmarsh's theorem for the first Hankel-Clifford transform in the space $L^p_\mu((0,+\infty))$”, Probl. Anal. Issues Anal., 11(29):3 (2022), 56–65 | DOI | MR

[6] Gogoladze L., Meskhia R., “On the absolute convergence of trigonometric Fourier series”, Proc. Razmadze Math. Inst., 141 (2006), 29–46 | MR

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

[8] Krayukhin S. A., Volosivets S. S., “Functions of bounded $p$-variation and weighted integrability of Fourier transforms”, Acta Math. Hung., 159:2 (2019), 374–399 | DOI | MR | Zbl

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

[10] Mahfoud A., El Hamma M., “Dini Clifford Lipschitz functions for the first Hankel-Clifford transform in the space $L^2_\mu$”, J. Anal., 30:3 (2022), 909–918 | DOI | MR

[11] Mendez J. M., La transformacion integral de Hankel-Clifford, Secretariado de Publicaciones de la Universidad de La Laguna, La Laguna, 1979

[12] 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

[13] Móricz F., “Sufficient conditions for the Lebesgue integrability of Fourier transforms”, Anal. Math., 36:2 (2010), 121–129 | DOI | MR | Zbl

[14] 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

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

[16] Platonov S. S., “On the Hankel transform of functions from Nikol'skii classes”, Integral Transforms Spec. Funct., 32:10 (2021), 823–838 | DOI | MR | Zbl

[17] 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

[18] 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

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

[20] Volosivets S., “Weighted integrability of Fourier-Dunkl transforms and generalized Lipschitz classes”, Analysis Math. Phys., 12 (2022), 115 | DOI | MR | Zbl

[21] Volosivets S. S., “Fourier-Bessel transforms and generalized uniform Lipschitz classes”, Integral Transforms Spec. Funct., 33:7 (2022), 559–569 | DOI | MR | Zbl

[22] Volosivets S. S., “Weighted integrability of Fourier-Jacobi transforms”, Integral Transforms Spec. Funct. (to appear) | DOI | MR

[23] Younis M.S., “Fourier transforms of Dini-Lipschitz functions”, Int. J. Math. Math. Sci., 9:2 (1986), 301–312 | DOI | MR | Zbl