The One-dimensional Martingale Hardy Spaces and Partial Sums and Fejér Means with respect to Walsh system

In this paper we prove and discuss some new $\left( H_p,L_{p}\right)$ type inequalities for partial Sums and Fejér means with respect to Walsh system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

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