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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ L\sp{p}$-behavior of power series with positive coefficients and Hardy spaces


Authors: Miodrag Mateljević and Miroslav Pavlović
Journal: Proc. Amer. Math. Soc. 87 (1983), 309-316
MSC: Primary 30D55
DOI: https://doi.org/10.1090/S0002-9939-1983-0681840-0
MathSciNet review: 681840
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Abstract: For the power series $ f(x) = \sum\nolimits_1^\infty {{a_n}{x^n}} $ with $ {a_n} \geqslant 0$, certain weighted $ {L^p}$-norms of $ f$ on $ [0,1]$ are estimated from above and below in terms of the coefficients $ {a_n}$. Some consequences of this are obtained. For example, some known results concerning Hardy spaces may be extended to a wider class of spaces.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0681840-0
Keywords: Hardy spaces, Hardy-Stein identity
Article copyright: © Copyright 1983 American Mathematical Society