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On the convergence of series in spaces of integrable functions. (English. Russian original) Zbl 1328.46025

Math. Notes 95, No. 6, 780-785 (2014); translation from Mat. Zametki 95, No. 6, 836-841 (2014).
Summary: A sufficient condition for the convergence of series in the spaces \(L_p\) on a set of infinite measure is obtained.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
26D15 Inequalities for sums, series and integrals
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References:

[1] V. Yu. Protasov, “Approximation by simple partial fractions and the Hilbert transform,” Izv. Ross. Akad. Nauk Ser. Mat. 73(2), 123-140 (2009) [Izv. Math. 73 (2), 333-349 (2009)]. · Zbl 1178.41010 · doi:10.4213/im2721
[2] I. R. Kayumov, “Convergence of series of simple partial fractions in <Emphasis Type=”Italic“>Lp(R),” Mat. Sb. 202(10), 87-98 (2011) [Sb. Math. 202 (10), 1493-1504 (2011)]. · doi:10.4213/sm7688
[3] G. Hardy, D. Littlewood, and G. Pólya, Inequalities (Cambridge Univ. Press, Cambridge, 1934; Inostr. Lit., Moscow, 1948). · JFM 60.0169.01
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