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Sbornik: Mathematics, 2011, Volume 202, Issue 10, Pages 1493–1504
DOI: https://doi.org/10.1070/SM2011v202n10ABEH004196 (Mi sm7688) 		 
This article is cited in 14 scientific papers (total 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
English version PDF (295 kB) Citations (14) Russian version article
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DOI: https://doi.org/10.1070/SM2011v202n10ABEH004196
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.
Received: 04.02.2010 and 08.04.2011
Bibliographic databases:
Document Type: Article
UDC: 517.538.52+517.444
MSC: Primary 41A20; Secondary 30B50
Language: English
Original paper language: Russian
Citation: I. R. Kayumov, “Convergence of series of simple partial fractions in $L_p(\mathbb R)$”, Sb. Math., 202:10 (2011), 1493–1504
Citation in format AMSBIB
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\paper Convergence of series of simple partial fractions in~$L_p(\mathbb R)$
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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