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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Equiconvergence theorems for Fourier-Bessel expansions with applications to the harmonic analysis of radial functions in Euclidean and non-Euclidean spaces


Authors: Leonardo Colzani, Antonio Crespi, Giancarlo Travaglini and Marco Vignati
Journal: Trans. Amer. Math. Soc. 338 (1993), 43-55
MSC: Primary 42B15
DOI: https://doi.org/10.1090/S0002-9947-1993-1108610-4
MathSciNet review: 1108610
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Abstract: We shall prove an equiconvergence theorem between Fourier-Bessel expansions of functions in certain weighted Lebesgue spaces and the classical cosine Fourier expansions of suitable related functions. These weighted Lebesgue spaces arise naturally in the harmonic analysis of radial functions on euclidean spaces and we shall use the equiconvergence result to deduce sharp results for the pointwise almost everywhere convergence of Fourier integrals of radial functions in the Lorentz spaces $ {L^{p,q}}({{\mathbf{R}}^n})$. Also we shall briefly apply the above approach to the study of the harmonic analysis of radial functions on noneuclidean hyperbolic spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1108610-4
Keywords: Fourier-Bessel expansions, Lorentz spaces, pointwise convergence
Article copyright: © Copyright 1993 American Mathematical Society