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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 2011 Volume 202, Number 10, Pages 87–98 (Mi sm7688)

This article is cited in 14 papers

Convergence of series of simple partial fractions in $L_p(\mathbb R)$

I. R. Kayumov

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: A necessary and sufficient condition for the series $\sum_{k=1}^\infty \frac{1}{t-z_k}$, $|z_k|<C |y_k|$, to converge in $L_p(\mathbb{R})$, $p>1$, is obtained.
Bibliography: 5 titles.

Keywords: simple partial fractions, Hardy's inequality, Fourier transform, Dirichlet series.

UDC: 517.538.52+517.444

MSC: Primary 41A20; Secondary 30B50

Received: 04.02.2010 and 08.04.2011

DOI: 10.4213/sm7688


 English version:
Sbornik: Mathematics, 2011, 202:10, 1493–1504

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© Steklov Math. Inst. of RAS, 2026