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Abstract  

Characterizations of the two-dimensional H 1, BMO and VMO martingale spaces generated by bounded Vilenkin systems via conjugate martingale transforms are studied.

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We prove the almost sure central limit theorem for martingales via an original approach which uses the Carleman moment theorem together with the convergence of moments of martingales. Several statistical applications to autoregressive and branching processes are also provided.

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Abstract  

Several interpolation theorems on martingale Hardy spaces over weighted measure spaces are given. Our proofs are based on the atomic decomposition of martingale Hardy spaces over weighted measure spaces. As applications of interpolation theorems, some inequalities of martingale transform operator are obtained.

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