Vol. 75, No. 2, 1978

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ISSN: 0030-8730
Fourier transforms and their Lipschitz classes

Gary Sampson and H. Tuy

Vol. 75 (1978), No. 2, 519–537
Abstract

We define a class of functions Aα for each α > 0. We show that the Fourier transform of every function of Aα exists and is Lipschitz of order α. We construct examples to show that the converse is not true in general. However, we show that for a certain class of function k (e.g., k L2) if its Fourier transform k is Lipschitz of order α then k Aβ for all β < α.

Mathematical Subject Classification 2000
Primary: 42A68, 42A68
Secondary: 42A20
Milestones
Received: 12 January 1976
Published: 1 April 1978
Authors
Gary Sampson
H. Tuy