✦ LIBER ✦

Radon, Cosine and Sine Transforms on Real Hyperbolic Space

✍ Scribed by Boris Rubin

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 186 KB
Volume: 170
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2002.2074

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✦ Synopsis

New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 14d4n À 1; in terms of polynomials of the Laplace-Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms.

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## Abstract In this paper, we pursue the study of harmonic functions on the real hyperbolic ball started in [13]. Our focus here is on the theory of Hardy‐Sobolev and Lipschitz spaces of these functions. We prove here that these spaces admit Fefferman‐Stein like characterizations in terms of maxima