(Hp−Lp)-Type inequalities for subsequences of Nörlund means of Walsh–Fourier series.

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 w e a k − L p for 0 < p < 1 / (1 + α) , where 0 < α < 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. [ABSTRACT FROM AUTHOR]