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An extension of the Hausdorff-Young theorem

Author: Robert M. Young
Journal: Proc. Amer. Math. Soc. 45 (1974), 235-236
MSC: Primary 42A16
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.

References [Enhancements On Off] (What's this?)

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  • [2] Yitzhak Katznelson, An introduction to harmonic analysis, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0248482
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Keywords: Exponential sums, separated sequence, almost periodic functions, interpolation of operators
Article copyright: © Copyright 1974 American Mathematical Society