This article is cited in 3 papers

The convergence of series of simple fractions in $L_p(\mathbb R)$.

A. V. Kayumova

Institute of Computer Mathematics and Information Technologies, Kazan (Volga Region) Federal University

Abstract: The convergence of series of simple fractions in $L_p(\mathbb R)$ has been investigated. In particular, necessary and sufficient conditions for the convergence of series with coefficients $\frac{p_k}{t-z_k}$, where $p_k$ is a sequence of positive numbers, in $L_p(\mathbb R)$ have been obtained.

Keywords: simple fractions, Hardy's inequality.

UDC: 517.538.52+517.444

Received: 16.01.2012