Author: F. Weisz 1
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  • 1 Eötvös L. University Department of Numerical Analysis Pázmány P. sétány 1/C. H-1117 Budapest Hungary
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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 fLp(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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