Tohoku Mathematical Journal
2001
September
SECOND SERIES VOL. 53, NO. 3

Tohoku Math. J.
53 (2001), 467-478

Title MEAN SQUARE DECAY OF FOURIER TRANSFORMS IN EUCLIDEAN AND NON EUCLIDEAN SPACES

Author Luca Brandolini, Leonardo Colzani and Andrea Torlaschi

(Received November 22, 1999, revised December 25, 2000)
Abstract. We study the asymptotic behavior of the quadratic means on spheres of increasing radius of the Fourier transforms of characteristic functions of sets with smooth boundary. Beside to give different proofs of known Euclidean results, we also consider the non-Euclidean Fourier transform on the two dimensional sphere and the hyperbolic disk.

2000 Mathematics Subject Classification. Primary 42B10. Secondary 43A30.

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