Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0364990
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)

  • [1] A. E. Ingham, Some trigonometrical inequalities with applications to the theory of series, Math. Z. 41 (1936), 367-379. MR 1545625
  • [2] Y. Katznelson, An introduction to harmonic analysis, Wiley, New York, 1968. MR 40 #1734. MR 0248482 (40:1734)
  • [3] R. Paley and N. Wiener, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., vol. 19, Amer. Math. Soc., Providence, R. I., 1934. MR 1451142 (98a:01023)
  • [4] E. C. Titchmarsh, A class of trigonometrical series, J. London Math. Soc. 3 (1928), 300-304.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A16

Retrieve articles in all journals with MSC: 42A16

Additional Information

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

American Mathematical Society