Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series

Authors:	Belov A S

Institution:	(1) Ivanovo State University, Russia

Abstract:	Fairly general conditions on the coefficients $\left\{ {a_n } \right\}_{n = 1}^\infty$ of even and odd trigonometric Fourier series under which L-convergence (boundedness) of partial sums of the series is equivalent to the relation $\sum\nolimits_{k = \left {{n \mathord{\left/ {\vphantom {n 2}} \right. \kern-\nulldelimiterspace} 2}} \right]}^{2n} {{{\left\| {a_k } \right\|} \mathord{\left/ {\vphantom {{\left\| {a_k } \right\|} {\left( {\left\| {n - k} \right\| + 1} \right) = o\left( 1 \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\left\| {n - k} \right\| + 1} \right) = o\left( 1 \right)}}} \left( { = O\left( 1 \right),{\text{ respectively}}} \right)$ are given.

Keywords:	trigonometric Fourier series L-convergence L-boundedness LC-sequence LB-sequence finitely lacunary sequence
本文献已被 SpringerLink 等数据库收录！