Vol. 21, No. 2, 1967

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Boundedness principles and Fourier theory

Robert E. Edwards

Vol. 21 (1967), No. 2, 255–263

A systematic application of simple functional analytic techniques (boundedness principles and the Hahn-Banach theorem) is made to establish a few results in harmonic analysis.

For the circle group, results are obtained about the possible misbehaviour of conjugate functions and related multiplier transforms.

For infinite compact Abelian groups, results are obtained about the possible misbehaviour of functions or pseudomeasures f for which the Fourier transform f is o(ρ), where ρ is a preassigned nonnegative function on the character group.

Mathematical Subject Classification
Primary: 42.50
Secondary: 42.52
Received: 20 August 1965
Published: 1 May 1967
Robert E. Edwards