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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An extension of the Hausdorff-Young theorem
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by Robert M. Young PDF
Proc. Amer. Math. Soc. 45 (1974), 235-236 Request permission

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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Additional Information
  • © Copyright 1974 American Mathematical Society
  • 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