Series with Monotone Coefficients by Walsh System

摘要

The paper studies the series ∞ ∑ n=0 a_nW_n(x) by Walsh system, where |a_n| monotone tends to zero and ∞ ∑ n=1 a_n~2=∞ .Some theorems on correction in L~1 and representability of functions from L~p, p ∈ (0,1) by subseries of the Walsh series are proved.