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 ∈ Lp(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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