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Almost everywhere convergence of Banach space-valued Vilenkin-Fourier series

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Abstract

The duality between martingale Hardy and BMO spaces is generalized for Banach space valued martingales. It is proved that if X is a UMD Banach space and f ∈ L p(X) for some 1 < p < ∞ then the Vilenkin-Fourier series of f converges to f almost everywhere in X norm, which is the extension of Carleson’s result.

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Authors and Affiliations

  1. Department of Numerical Analysis, Eötvös L. University, Pázmány P. sétány 1/C., H-1117, Budapest, Hungary

    F. Weisz

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  1. F. Weisz
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This paper was written while the author was researching at University of Vienna (NuHAG) supported by Lise Meitner fellowship No. M733-N04. This research was also supported by the Hungarian Scientific Research Funds (OTKA) No. T043769, T047128, T047132.

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Weisz, F. Almost everywhere convergence of Banach space-valued Vilenkin-Fourier series. Acta Math Hung 116, 47–59 (2007). https://doi.org/10.1007/s10474-007-5289-1

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  • DOI: https://doi.org/10.1007/s10474-007-5289-1

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