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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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 improved Menshov-Rademacher theorem
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by Ferenc Móricz and Károly Tandori PDF
Proc. Amer. Math. Soc. 124 (1996), 877-885 Request permission

Abstract:

We study the a.e. convergence of orthogonal series defined over a general measure space. We give sufficient conditions which contain the Menshov-Rademacher theorem as an endpoint case. These conditions turn out to be necessary in the particular case where the measure space is the unit interval $[0,1]$ and the moduli of the coefficients form a nonincreasing sequence. We also prove a new version of the Menshov-Rademacher inequality.
References
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Additional Information
  • Ferenc Móricz
  • Affiliation: Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, 6720 Szeged, Hungary
  • Email: moricz@math.u-szeged.hu
  • Károly Tandori
  • Affiliation: Bolyai Institute, University of Szeged, Aradi Vértanúk Tere 1, 6720 Szeged, Hungary
  • Received by editor(s): November 1, 1993
  • Received by editor(s) in revised form: September 26, 1994
  • Additional Notes: This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant #234
  • Communicated by: J. Marshall Ash
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 877-885
  • MSC (1991): Primary 42C05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03151-6
  • MathSciNet review: 1301040