On integrability of weighted sums of series with respect to multiplicative systems

In this paper we consider the series with respect to multiplicative systems Σk=1∞ bkxk(x) with non-negative coefficients tending to zero, quasi-monotone coefficients and coefficients of class R0+BV S.It is shown, that there exists the sum f (x) for such series on [0, 1]. We study the problem of inte...

Full description

Saved in:
Bibliographic Details
Main Authors: Gulmira, Kenzhebekova, Zauresh, Suleimenova
Format: Conference Proceeding
Language:English
Subjects:
Coefficients
Integral calculus
Sums
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider the series with respect to multiplicative systems Σk=1∞ bkxk(x) with non-negative coefficients tending to zero, quasi-monotone coefficients and coefficients of class R0+BV S.It is shown, that there exists the sum f (x) for such series on [0, 1]. We study the problem of integrability of weighted sums of the series. Sufficient conditions to weighted function φ(x) for which φ(x) f (x) ∈ L[0, 1) and φ(x) f (x) ∈ Lp[0, 1), 1 < p < ∞ are found.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4930514