Geodesic
Convergence of series of simple partial fractions in~$L_p(\mathbb R)$
Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1493-1504

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A necessary and sufficient condition for the series $\sum_{k=1}^\infty \frac{1}{t-z_k}$, $|z_k|$, to converge in $L_p(\mathbb{R})$, $p>1$, is obtained. Bibliography: 5 titles.
Keywords: Hardy's inequality, Dirichlet series.
Mots-clés : simple partial fractions, Fourier transform 
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     author = {I. R. Kayumov},
     title = {Convergence of series of simple partial fractions in~$L_p(\mathbb R)$},
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     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_10_a3/}
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I. R. Kayumov. Convergence of series of simple partial fractions in~$L_p(\mathbb R)$. Sbornik. Mathematics, Tome 202 (2011) no. 10, pp. 1493-1504. http://geodesic.mathdoc.fr/item/SM_2011_202_10_a3/