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.
- Atomic decomposition
- UMD spaces
- Vector-valued Hardy and BMO spaces
- Vector-valued Vilenkin-Fourier series
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