Spaces of 𝒟_{ℒ^{𝓅}}-type and the Hankel convolution

Betancor, J.; González, B.

doi:10.1090/S0002-9939-00-05583-0

Spaces of ${\mathcal D}_{L^p}-$type and the Hankel convolution
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by J. J. Betancor and B. J. González PDF

Proc. Amer. Math. Soc. 129 (2001), 219-228 Request permission

Abstract:

In this paper we introduce new function spaces that are denoted by ${\mathcal H}_{\mu ,p}$, $\mu >-1/2$ and $1\leq p\leq \infty ,$ and that are spaces of ${\mathcal D}_{L^{p}}-$type where the Hankel convolution and the Hankel transformation are defined. The spaces ${\mathcal H}_{\mu ,p}$ will play the same role in the Hankel setting that the spaces ${\mathcal D}_{L^{p}}$ play in the theory of Fourier transformation.

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