Geodesic
The convergence of series of simple fractions in $L_p(\mathbb R)$.
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 208-213

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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.
Mots-clés : simple fractions
Keywords: Hardy's inequality. 
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     author = {A. V. Kayumova},
     title = {The convergence of series of simple fractions in $L_p(\mathbb R)$.},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {208--213},
     publisher = {mathdoc},
     volume = {154},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a18/}
}
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A. V. Kayumova. The convergence of series of simple fractions in $L_p(\mathbb R)$.. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 208-213. http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a18/