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Almost everywhere convergence of lacunary partial sums of Vilenkin-Fourier series
Author(s):
Wo-Sang
Young
Journal:
Proc. Amer. Math. Soc.
124
(1996),
3789-3795.
MSC (1991):
Primary 42C10;
Secondary 42B25, 43A75
MathSciNet review:
1346995
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Abstract:
We prove that if  , and  is any lacunary sequence of positive integers, then the sequence of  th partial sums of Vilenkin-Fourier series of  converges almost everywhere to  .
References:
- 1.
- D.L. Burkholder, Distribution function inequalities for martingales, Ann. Probab. 1 (1973), 19-42. MR 51:1944
- 2.
- P. Simon, On the concept of a conjugate function, Colloq. Math. Soc. J. Bolyai, Fourier Analysis and Approximation Theory, 1976 19 (1978), 747-755. MR 81b:42084
- 3.
- P. Simon, On a maximal function, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 21 (1978), 41-44. MR 81b:42083
- 4.
- W.-S. Young, Mean convergence of generalized Walsh-Fourier series, Trans. Amer. Math. Soc. 218 (1976), 311-320. MR 52:14828
- 5.
- W.-S. Young, Almost everywhere convergence of Vilenkin-Fourier series of
 -functions, Proc. Amer. Math. Soc. 108 (1990), 433-441. MR 90g:42057 - 6.
- W.-S. Young, Littlewood-Paley and multiplier theorems for Vilenkin-Fourier series, Canad. J. Math. 46 (1994), 662-672. MR 95c:42031
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Additional Information:
Wo-Sang
Young
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
DOI:
10.1090/S0002-9939-96-03566-6
PII:
S 0002-9939(96)03566-6
Received by editor(s):
March 8, 1995
Received by editor(s) in revised form:
June 15, 1995
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1996,
American Mathematical Society
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