Universal Walsh Series with Monotone Coefficients in Weighted Lp Spaces
Martin Grigoryan *
Chair of Higher Mathematics, Yerevan State University, 1, Alex Manoogian str., 0025, Yerevan, Republic of Armenia.
Zaruhi Davtyan
Department of Applied Mathematics and Information, Russian-Armenian (Slavonic) University, 123 Hovsep Emin str., 0051, Yerevan, Republic of Armenia.
*Author to whom correspondence should be addressed.
Abstract
For any 0 < δ < 1 there exists a measurable function μ(x), 0 < μ(x) ≤ 1,
with | {x ∈ [0, 1]; μ(x) ≠ 1} |< δ, and a series in the Walsh system 
of the form
such that for any p ≥ 1 and any function 
one can fined subseries of above series
converging 
Keywords: Walsh system, convergence, weighted spaces.