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Spaces of type and the Hankel convolution

Authors:	J J Betancor B J Gonzá lez

Institution:	Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Islas Canarias, Spain ; Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Islas Canarias, Spain

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.

Keywords:	${\mathcal D}_{L^p}-$spaces Hankel convolution Bessel operator

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