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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spaces of ${\mathcal D}_{L^p}-$type and the Hankel convolution


Authors: J. J. Betancor and B. J. González
Journal: Proc. Amer. Math. Soc. 129 (2001), 219-228
MSC (2000): Primary 46F12
Published electronically: August 17, 2000
MathSciNet review: 1707136
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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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Additional Information

J. J. Betancor
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Islas Canarias, Spain
Email: jbetanco@ull.es

B. J. González
Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Islas Canarias, Spain

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05583-0
PII: S 0002-9939(00)05583-0
Keywords: ${\mathcal D}_{L^p}-$spaces, Hankel convolution, Bessel operator
Received by editor(s): January 16, 1998
Received by editor(s) in revised form: April 6, 1999
Published electronically: August 17, 2000
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society