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An improved Menshov-Rademacher theorem


Authors: Ferenc Móricz and Károly Tandori
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
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-96-03151-6
Keywords: Orthonormal system, a.e. convergence, Menshov-Rademacher inequality and theorem
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
Article copyright: © Copyright 1996 American Mathematical Society