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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on two weight function conditions for a Fourier transform norm inequality


Author: Benjamin Muckenhoupt
Journal: Proc. Amer. Math. Soc. 88 (1983), 97-100
MSC: Primary 42A45; Secondary 42A50
MathSciNet review: 691285
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Abstract: Recent papers have given two different conditions on pairs of nonnegative weight functions that insure that a Fourier transform norm inequality holds in $ {{\mathbf{R}}^n}$. With additional assumptions these conditions were also shown to be implied by the norm inequality. A direct proof is given here that these conditions are equivalent; this can be used to simplify some of the proofs in those papers.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0691285-5
PII: S 0002-9939(1983)0691285-5
Article copyright: © Copyright 1983 American Mathematical Society