Local uncertainty inequalities for Fourier series
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- by John F. Price and Paul C. Racki PDF
- Proc. Amer. Math. Soc. 93 (1985), 245-251 Request permission
Abstract:
Necessary and sufficient conditions are given on $\alpha$, $\beta$ and $t$ for there to exist a constant $K$ such that \[ {\left ( {{{\sum \limits _{n \in E} {\left | {\hat f(n)} \right |} }^2}} \right )^{1/2}} \leqslant K{\left | E \right |^\alpha }{\left \| {f{{\left | x \right |}^\beta }} \right \|_t}\] for all $f \in {L^1}({T^d})$ and finite $E \subset {Z^d}$.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 245-251
- MSC: Primary 42A38; Secondary 26D15, 42A05
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770530-3
- MathSciNet review: 770530