A multiplier theorem

Louis Pigno

Vol. 34 (1970), No. 3, 755–757

DOI: 10.2140/pjm.1970.34.755

Abstract

Let G be a locally compact abelian group and φ a complex-valued function defined on the dual Γ. In this paper we prove that φ is a multiplier of type (L¹ ∩ L^∞,L¹ ∩ C) if and only if φ = f for some f ∈ L¹(G).

Mathematical Subject Classification

Primary: 42.55

Milestones

Received: 10 December 1969

Published: 1 September 1970