Abstract
We investigate the subsequence {t_{2^{n}}f } of Nörlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H_{p} to the space mathit{weak-}L_{p} for 0< p<1/(1+alpha ) , where 0<alpha <1. Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Nörlund logarithmic means and Cesàro means.
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