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

F. Weisz

doi:10.1007/s10474-007-5289-1

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Acta Mathematica Hungarica

Volume/Issue:: Volume 116: Issue 1-2

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

Author: F. Weisz¹

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

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

Page Count:: 47–59

Publication Date:: 01 Jul 2007

Online Publication Date:: 23 Feb 2007

Article Category:: Research Article

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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.