# Growth Properties of the Cherednik-Opdam Transform in the Space Lp

Document Type: Research articles

Authors

1 FACULTE OF SCIENCE

2 University Hassan II, Casablanca, Morocco

Abstract

‎In this paper‎, ‎using a generalized translation operator‎, ‎we obtain a generalization of Younis Theorem 5.2 in [3] for the Cherednik-Opdam transform for functions satisfying the $(\delta,\gamma,p)$-Cherednik-Opdam Lipschitz condition in the space‎ ‎$L^{p}_{\alpha,\beta}(\mathbb{R})$.

Keywords

Article Title [Persian]

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Abstract [Persian]

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### References

[1] E. M. Opdam, Harmonic analysis for certain representations of graded Hecke algebras,Acta Math. 175(2)(1995), 75121.
[2] J. P. Anker, F. Ayadi, and M. Si , Opdams hypergeometric functions: product formula and convolution structure in dimension 1, Adv. Pure Appl. Math. 3(1) (2012), 1144.
[3] M. S. Younis , Fourier Transforms of Dini-Lipschitz Functions. Int. J. Math. Math. Sci. 9 (2),(1986), 301312. doi:10.1155/S0161171286000376.
[4] S. S. Platonov, Approximation of functions in L2-metric on noncompact rank 1 symmetric space . Algebra Analiz .11(1) (1999), 244-270.
[5] T. R. Johansen, Remarks on the inverse Cherednik-Opdam transform on the real line, arXiv:1502.01293v1 (2015).
[6] M. L. Mittal and V. N. Mishra, Approximation of signals (functions) belonging to the Weighted W(Lp; (t)), (p  1)-Class by almost matrix summability method of its Fourier series, Int. J. of Math. Sci. and Engg.
Appls. 2 (2008), No. IV, 1- 9.
[7] V. N. Mishra, K. Khatri, and L. N. Mishra, Product (N; pn)(E; q) summability of a sequence of Fourier coecients, Mathematical Sciences (Springer open access) 6:38 (2012), DOI: 10.1186/2251 7456-6-38.
[8] V. N. Mishra, K. Khatri, and L. N. Mishra, Using linear operators to approximate signals of Lip( ; p), (p  1)-class, Filomat 27:2 (2013), 355-365.
[9] V. N. Mishra, K. Khatri, and L. N. Mishra, Product summability transform of conjugate series of Fourier series, International Journal of Mathematics and Mathematical Sciences Article ID 298923 (2012), 13 pages, DOI: 10.1155/2012/298923.
[10] V. N. Mishra, K. Khatri, and L. N. Mishra, Approximation of functions belonging to Lip((t); r) class by (N; pn)(C; 1) summability of conjugate series of Fourier series, Journal of Inequalities and Applications (2012), doi:10.1186/1029-242X-2012-296.
[11] L. N. Mishra, V. N. Mishra, K. Khatri, and Deepmala, On the trigonometric approximation of signals belonging to beneralized weighted lipschitz Lip((t); r), r  1, class by matrix (C1;Np) operator of conjugate series of its Fourier series, Applied Mathematics and Computation, 237 (2014) 252263. DOI: 10.1016/j.amc.2014.03.085.
[12] V. N. Mishra and L. N. Mishra, Trigonometric approximation in Lp, (p  1)-spaces. Int. J. Contemp. Math. Sci. 7, 909-918 (2012).