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