J Austral Math Soc Ser A 43 pp385--397, 1987.

Motion Groups and Absolutely Convergent Fourier Transforms

Garth I. Gaudry and Rita Pini

Abstract

According to an extension of a classical theorem of Bernstein, due to C. Herz, a function on Rⁿ belonging to a Besov space of appropriate order has an absolutely convergent Fourier transform. We establish extensions of this result to Cartan motion groups, for Besov spaces defined with repect to both isotropic and non-isotropic differences.

1980 AMS Subject Classification: 22E30, 41A17, 43A50, 43A80

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Authors

Garth I. Gaudry

School of Mathematical Sciences, The Flinders University of South Australia, Bedford Park S.A. 5042, Australia.

Rita Pini

Via Lattanzio 16, 20127 Milano, Italy.