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On power series with positive coefficients

О стЕпЕННых РьДАх с пО лОжИтЕльНыМИ кОЁФФИ цИЕНтАМИ

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слЕДУь ИДЕЕ M. МАтЕлЕВИ ЧА И М. пАВлОВИЧА, Мы ОБ ОБЩАЕМ НЕкОтОРыЕ клАссИЧЕс кИЕ НЕРАВЕНстВА хАРДИ И л ИттлВУДА. гРУБО гОВОР ь, ФУНкцИИх α Их p В НЕРАВЕНстВАх хАРДИ И лИттлВУДА жАМЕНьУтс ь НА БОлЕЕ ОБЩИЕ ФУНкцИИА(х) И Φ(х). кРОМЕ тОгО, ИспОль жУь тАк НАжыВАЕМыИ “Б лОЧНыИ МЕтОД”, Мы пРИхОДИМ к НЕкОтОРОМУ НЕБОльшО МУ УлУЧшЕНИУ И В клАсс ИЧЕскОМ слУЧАЕ.

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References

  1. G. H. Hardy andJ. E. Littlewood, Elementary theorems concerning power series with positive coefficients and moment constants of positive functions,J. für Math.,157(1927), 141–158.

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  2. L. Leindler, Generalizations of some theorems of Hardy and Littlewood concerning power series and moment constants,Analysis Math.,19(1993), 135–149.

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  3. M. Mateljevic andM. Pavlovic,L p-behavior of power series with positive coefficients and Hardy spaces,Proc. Amer. Math. Soc.,87(1983), 309–316.

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Leindler, L. On power series with positive coefficients. Analysis Mathematica 20, 205–211 (1994). https://doi.org/10.1007/BF01924093

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