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Negzaoui, Selma; Sifi, Mohamed

On partial Fourier-Bessel operator in higher dimension. (English) Zbl 1442.42033

Integral Transforms Spec. Funct. 31, No. 6, 424-436 (2020).
Summary: In this paper, we consider the Bessel Fourier transform on the Weyl chamber which generalizes Hankel transform and coincides with the restriction of the Dunkl transform associated to the reflection group \(B_q = S_q \ltimes \mathbb Z^q_2\). We deal with partial Bessel integrals and we give an interesting estimation of the modified partial Bessel integrals on \(L^2(\tilde{\omega}_\mu) \cap L^\infty(\tilde{\omega}_\mu)\).

Cited in 1 Document

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
33C70 Other hypergeometric functions and integrals in several variables

Keywords:

multi-variable Bessel functions; Bochner-Riesz means; Dunkl transform on the Weyl chamber; Hausdorff-Young inequality; symmetric cone
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References:

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