RUS
ENG
Full version
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
Fulltext:
PDF file (485 kB)
References
Cited by
English version:
Sbornik: Mathematics, 2011,
202
:10,
1493–1504
Bibliographic databases:
©
Steklov Math. Inst. of RAS
, 2026