Solvability of convolution equations in 𝒦′_p, p > 1

S. Sznajder and Zbigniew Zielezny

Vol. 63 (1976), No. 2, 539–544

DOI: 10.2140/pjm.1976.63.539

Abstract

Let S be a convolution operator in the space 𝒦_p′, p > 1, of distributions in Rⁿ growing no faster than exp(k|x|^p) for some k. A condition on S introduced by I. Cioranescu is proved to be equivalent to S ∗𝒦_p′ = 𝒦_p′.

Mathematical Subject Classification 2000

Primary: 46F10

Secondary: 47B37

Milestones

Received: 24 September 1975

Revised: 4 February 1976

Published: 1 April 1976