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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An extension of the Hausdorff-Young theorem


Author: Robert M. Young
Journal: Proc. Amer. Math. Soc. 45 (1974), 235-236
MSC: Primary 42A16
DOI: https://doi.org/10.1090/S0002-9939-1974-0364990-2
MathSciNet review: 0364990
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Abstract: Using the Riesz-Thorin interpolation theorem, we show that if $1 < p < 2$ and $f$ belongs to ${L^p}( - \pi ,\pi )$, then $\{ \hat f({z_n})\}$ belongs to ${l^q}(q = p/(p - 1))$ for a very general class of complex sequences $\{ {z_n}\}$. We also obtain a convergence criterion for a related class of exponential sums.


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Keywords: Exponential sums, separated sequence, almost periodic functions, interpolation of operators
Article copyright: © Copyright 1974 American Mathematical Society