Generalized Hausdorff-Young inequalities and mixed norm spaces

Lynn Roy Williams

Vol. 38 (1971), No. 3, 823–833

DOI: 10.2140/pjm.1971.38.823

Abstract

We generalize the Hausdorff-Young Theorem for a locally compact connected group G by showing that if f ∈ L^p(G),1 < p ≦ 2, then the Fourier transform of f is in a mixed norm space properly contained in L^pJ(Γ), where Γ is the dual group and 1∕p + 1∕p′ = 1. In the last section we apply the above theorem to obtain new results concerning sets of uniqueness for functions in L^p(G), and we give new sufficient conditions which insure that the product of a continuous function and a pseudomeasure is the zero distribution.

Mathematical Subject Classification 2000

Primary: 43A45

Milestones

Received: 6 October 1970

Published: 1 September 1971