Vol. 38, No. 3, 1971

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Generalized Hausdorff-Young inequalities and mixed norm spaces

Lynn Roy Williams

Vol. 38 (1971), No. 3, 823–833

We generalize the Hausdorff-Young Theorem for a locally compact connected group G by showing that if f Lp(G),1 < p 2, then the Fourier transform of f is in a mixed norm space properly contained in LpJ(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 Lp(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
Received: 6 October 1970
Published: 1 September 1971
Lynn Roy Williams