A Tauberian theorem for Vilenkin series
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- by W. R. Wade PDF
- Proc. Amer. Math. Soc. 131 (2003), 2877-2881 Request permission
Abstract:
There are a number of papers in the literature which contain Cesàro analogues of results already known for martingale sums of Vilenkin-Fourier series. We show that for Vilenkin systems of bounded type, these are not merely analogues but actually generalizations. Indeed, we prove that convergence of the Cesàro means of a Vilenkin series $S$ implies convergence of martingale partial sums of $S$ itself.References
- James E. Daly and Keith L. Phillips, A note on $H^1$ multipliers for locally compact Vilenkin groups, Canad. Math. Bull. 41 (1998), no. 4, 392–397. MR 1658219, DOI 10.4153/CMB-1998-052-0
- Walter Rudin, Real and complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1987. MR 924157
- L.A. Shaginyan, On definite limits and sets of limit functions of Walsh series, Mat. Sbornik 95 (1974), 263–271.
- Garrett Birkhoff and Morgan Ward, A characterization of Boolean algebras, Ann. of Math. (2) 40 (1939), 609–610. MR 9, DOI 10.2307/1968945
Additional Information
- W. R. Wade
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- Received by editor(s): April 10, 2002
- Published electronically: February 28, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 2877-2881
- MSC (2000): Primary 42C10, 43A75
- DOI: https://doi.org/10.1090/S0002-9939-03-07044-8
- MathSciNet review: 1974345