A representation theorem for convolution transform with determining function in L^p

Victor Dannon and Dany Leviatan

Vol. 62 (1976), No. 1, 81–86

DOI: 10.2140/pjm.1976.62.81

Abstract

Let G(t) be a kernel in Class II. Necessary conditions in order that a function f(x) be the convolution transform of ϕ(t) ∈ L^p(−∞,∞) were obtained by the second author. Also it was conjectured that the conditions are in fact sufficient. The conjecture is indeed true and we prove it here.

Mathematical Subject Classification 2000

Primary: 44A35

Milestones

Received: 3 June 1974

Published: 1 January 1976