Geodesic
Generalization of Titchmarsh'~s theorem for the first Hankel-Clifford transform in the space {\boldmath${L^{p}_{\mu}}((0,+\infty))$}
Problemy analiza, Tome 11 (2022) no. 3, pp. 56-65.

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Using a generalized translation operator, we intend to establish generalizations of the Titchmarsh theorem ([ref14], theorem 84) for the first Hankel-Clifford transform for certain classes of functions in the space $L^{p}_{\mu}((0,+\infty))$, where $1$.
Keywords: first Hankel-Clifford transform, generalized translation operator, Clifford-Lipschitz class, Dini-Clifford-Lipschitz class. 
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     author = {M. El Hamma and A. Mahfoud},
     title = {Generalization of {Titchmarsh'~s} theorem for the first {Hankel-Clifford} transform in the space {\boldmath${L^{p}_{\mu}}((0,+\infty))$}},
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M. El Hamma; A. Mahfoud. Generalization of Titchmarsh'~s theorem for the first Hankel-Clifford transform in the space {\boldmath${L^{p}_{\mu}}((0,+\infty))$}. Problemy analiza, Tome 11 (2022) no. 3, pp. 56-65. http://geodesic.mathdoc.fr/item/PA_2022_11_3_a4/

[1] Abilov V. A., Abilova F. V., “Approximation of Functions by Fourier-Bessel sums”, IZV. Vyssh. Uchebn Zaved. Mat., 2001, no. 8, 3–9 | MR | Zbl

[2] Daher R., Djellab N., El Hamma M., “Some theorems of the Jacobi-Lipshitz class for the Jacobi transform”, Bulletin of the Transilvania University of Brasov, Series III: Mathematics and Computer Science, 1(63):2 (2021), 29–36 | DOI | MR

[3] Daher R., El Hamma M., Akhlidj A. Dini-Lipschitz functions for the Bessel transform, Nonlinear studies, 24:2 (2017), 297–301 | MR | Zbl

[4] Daher R., Tyr O., Growth properties of the q-Dunkl transform in the space $L^{p}_{q,\alpha}(\mathbb{R}_{q}, \vert x\vert^{2\alpha+1}d_{q}x)$, 57:1 (2022), 119–134 | MR | Zbl

[5] El Hamma M., Daher R., On some theorems of the Dunkl-Lipschitz class for the Dunkl transform, 40:8 (2019), 1157–1163 | MR | Zbl

[6] Gray A., Matthecos G. B., MacRobert T. M., A Treatise on Bessel functions and their applications to physics, Macmillan, London, 1987 | MR

[7] Haimo D. T., “Integral equations associated with Hankel convolution”, Trans. Amer. Math. Soc., 116 (1965) | DOI | MR | Zbl

[8] Malgonde S. P., Bandewar S. R., “On the generalized Hankel-Clifford transformation of arbitrary order”, Proc. Indian Alod Sci. Math Sci., 110:3 (2000), 293–304 | 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 (1991), 543–557 | DOI | MR | Zbl

[10] Negzaoui S., “Lipschitz conditions in Lagurre Hypergroup”, Mediterr. J. Math., 14 (2017), 191 | DOI | MR | Zbl

[11] Prasad A., Kumar M., “Continuity of pseu-differential operator $h_{1,\mu }$, involving Hankel translation and Hankel convolution some Gevrey spaces”, Integral. Transforms Spec. Funct., 21:6 (2010), 465–477 | DOI | MR | Zbl

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

[13] Pathak R. S., Pandey P. K., “A class of pseudo-differential operator associated with Bessel operators”, J. Math. Anal. Appl., 196 (1995), 736–747 | DOI | MR | Zbl

[14] Titchmarsh E. C., Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1948 | MR

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

[16] Zemanian A. H., Generalized integral transformations, Interscience Publishers, New York, 1968 | MR | Zbl