Weighted norm inequalities for the Fourier transform on certain totally disconnected groups

Author:
T. S. Quek

Journal:
Proc. Amer. Math. Soc. **101** (1987), 113-121

MSC:
Primary 43A70

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897080-X

MathSciNet review:
897080

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a locally compact totally disconnected Abelian group with dual group . Let and be nonnegative measurable functions on and , respectively. In this paper we give, in terms of and , a necessary condition and some sufficient conditions for the inequality to hold for all in , where denotes the Fourier transform of and . If and are both radial, we give a necessary and sufficient condition for the above norm inequality to hold for all in .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0897080-X

Article copyright:
© Copyright 1987
American Mathematical Society