Fourier transforms and their Lipschitz classes

Gary Sampson and H. Tuy

Vol. 75 (1978), No. 2, 519–537

DOI: 10.2140/pjm.1978.75.519

Abstract

We define a class of functions A_α for each α > 0. We show that the Fourier transform of every function of A_α 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 ∈ A_β for all β < α.

Mathematical Subject Classification 2000

Primary: 42A68, 42A68

Secondary: 42A20

Milestones

Received: 12 January 1976

Published: 1 April 1978