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El Hamma, Mohamed; Lafdal, Hamad Sidi; Djellab, Nisrine; Khalil, Chaimaa

Jacobi transform of \((\nu, \gamma, p)\)-Jacobi-Lipschitz functions in the space \(\text{L}^p(\mathbb{R}^+,\Delta_{(\alpha,\beta)}(t) dt)\). (English) Zbl 1443.42005

Ural Math. J. 5, No. 1, 53-58 (2019).
Summary: Using a generalized translation operator, we obtain an analog of Younis’ theorem [M. S. Younis, Int. J. Math. Math. Sci. 9, 301–312 (1986; Zbl 0595.42006), Theorem 5.2] for the Jacobi transform for functions from the \((\nu, \gamma, p)\)-Jacobi-Lipschitz class in the space \(\text{L}^p(\mathbb{R}^+,\Delta_{(\alpha,\beta)}(t)dt)\).

MSC:

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
43A85 Harmonic analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)

Keywords:

Jacobi operator; Jacobi transform; generalized translation operator

Citations:

Zbl 0595.42006
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\textit{M. El Hamma} et al., Ural Math. J. 5, No. 1, 53--58 (2019; Zbl 1443.42005)
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