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

 

Local uncertainty inequalities for Fourier series


Authors: John F. Price and Paul C. Racki
Journal: Proc. Amer. Math. Soc. 93 (1985), 245-251
MSC: Primary 42A38; Secondary 26D15, 42A05
MathSciNet review: 770530
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Abstract: Necessary and sufficient conditions are given on $ \alpha $, $ \beta $ and $ t$ for there to exist a constant $ K$ such that

$\displaystyle {\left( {{{\sum\limits_{n \in E} {\left\vert {\hat f(n)} \right\v... ...vert^\alpha }{\left\Vert {f{{\left\vert x \right\vert}^\beta }} \right\Vert _t}$

for all $ f \in {L^1}({T^d})$ and finite $ E \subset {Z^d}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770530-3
PII: S 0002-9939(1985)0770530-3
Article copyright: © Copyright 1985 American Mathematical Society