Proceedings of the Japan Academy, Series A, Mathematical Sciences

Dunkl transform of $(\beta, \gamma)$-Dunkl Lipschitz functions

Radouan Daher, Mustapha Boujeddaine, and Mohamed El Hamma

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Abstract

In this paper, we obtain an analog of Younis’s Theorem 5.2 in~[7] for the Dunkl transform on the real line for functions satisfying the $(\beta, \gamma)$-Dunkl Lipschitz condition in the space $\mathrm{L}^{p}(\mathbf{R}, |x|^{2\alpha+1}dx)$, where $\alpha\geq -\frac{1}{2}$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 9 (2014), 135-137.

Dates
First available in Project Euclid: 6 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1415285008

Digital Object Identifier
doi:10.3792/pjaa.90.135

Mathematical Reviews number (MathSciNet)
MR3277206

Zentralblatt MATH identifier
1334.46023

Subjects
Primary: 46E30; 41A25; 41A17

Keywords
Dunkl operator Dunkl transform generalized translation operator

Citation

Daher, Radouan; Boujeddaine, Mustapha; El Hamma, Mohamed. Dunkl transform of $(\beta, \gamma)$-Dunkl Lipschitz functions. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 9, 135--137. doi:10.3792/pjaa.90.135. https://projecteuclid.org/euclid.pja/1415285008


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References

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