Geodesic
Integral bounds for simple partial fractions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 33-45

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For $p\ge2$ we obtain bounds of $L_p$-norms of the Fourier transform of real parts of simple partial fractions. For even $p$ our estimate is sharp. We also prove a new inequality for $L_p$-norms of simple partial fractions which in some cases is stronger than the corresponding inequality obtained by V. Yu. Protasov.
Mots-clés : simple partial fractions, Fourier transform
Keywords: Hausdorff–Young inequality, Dirichlet series. 
@article{IVM_2012_4_a3,
     author = {I. R. Kayumov},
     title = {Integral bounds for simple partial fractions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--45},
     publisher = {mathdoc},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_4_a3/}
}
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I. R. Kayumov. Integral bounds for simple partial fractions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2012), pp. 33-45. http://geodesic.mathdoc.fr/item/IVM_2012_4_a3/