On the Convergence of Partial Sums with Respect to Vilenkin System on the Martingale Hardy Spaces

摘要

In this paper, we derive characterizations of boundedness of subsequences of partial sums with respect to Vilenkin system on the martingale Hardy spaces H-p when 0 p 1. Moreover, we find necessary and sufficient conditions for the modulus of continuity of martingales f is an element of H-p, which provide convergence of subsequences of partial sums on the martingale Hardy spaces H-p. It is also proved that these results are the best possible in a special sense. As applications, some known and new results are pointed out.