Arithmetic means of Walsh-Fourier partial sums converge almost everywhere for sequences satisfying a(n+1) ≥ (1 + n^{-δ})a(n) when 0<δ<1, extending the prior range of δ<1/2.
Gát,On the convergence of Fejér means of some subsequences of partial sums of Walsh–Fourier series, Ann
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Almost Everywhere Convergence of Arithmetic Means of Walsh--Fourier Partial Sums Along Subsequences
Arithmetic means of Walsh-Fourier partial sums converge almost everywhere for sequences satisfying a(n+1) ≥ (1 + n^{-δ})a(n) when 0<δ<1, extending the prior range of δ<1/2.