Spaces of ${\mathcal D}_{L^p}-$type and the Hankel convolution
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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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 219-228
- MSC (2000): Primary 46F12
- DOI: https://doi.org/10.1090/S0002-9939-00-05583-0
- MathSciNet review: 1707136