Almost everywhere convergence of lacunary partial sums of Vilenkin-Fourier series
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Abstract:
We prove that if $f\in L^{p},\;p>1$, and $\{n_{k}\}$ is any lacunary sequence of positive integers, then the sequence of $n_{k}$th partial sums of Vilenkin-Fourier series of $f$ converges almost everywhere to $f$.References
- D. L. Burkholder, Distribution function inequalities for martingales, Ann. Probability 1 (1973), 19–42. MR 365692, DOI 10.1214/aop/1176997023
- P. Simon, On the concept of a conjugate function, Fourier analysis and approximation theory (Proc. Colloq., Budapest, 1976) Colloq. Math. Soc. János Bolyai, vol. 19, North-Holland, Amsterdam-New York, 1978, pp. 747–755. MR 540350
- P. Simon, On a maximal function, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 21 (1978), 41–44 (1979). MR 536200
- Wo Sang Young, Mean convergence of generalized Walsh-Fourier series, Trans. Amer. Math. Soc. 218 (1976), 311–320. MR 394022, DOI 10.1090/S0002-9947-1976-0394022-8
- Wo-Sang Young, Almost everywhere convergence of Vilenkin-Fourier series of $H^1$ functions, Proc. Amer. Math. Soc. 108 (1990), no. 2, 433–441. MR 998742, DOI 10.1090/S0002-9939-1990-0998742-6
- Wo-Sang Young, Littlewood-Paley and multiplier theorems for Vilenkin-Fourier series, Canad. J. Math. 46 (1994), no. 3, 662–672. MR 1276118, DOI 10.4153/CJM-1994-036-3
Additional Information
- Wo-Sang Young
- Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Received by editor(s): March 8, 1995
- Received by editor(s) in revised form: June 15, 1995
- Communicated by: J. Marshall Ash
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3789-3795
- MSC (1991): Primary 42C10; Secondary 42B25, 43A75
- DOI: https://doi.org/10.1090/S0002-9939-96-03566-6
- MathSciNet review: 1346995