On a theorem of Hardy and Littlewood
Author:
Luis G. Bernal
Journal:
Proc. Amer. Math. Soc. 104 (1988), 10781080
MSC:
Primary 40E05; Secondary 30B10, 30B30
MathSciNet review:
931724
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Abstract: In this paper, we give an extension of a classical theorem of Hardy and Littlewood on power series. Let be a strictly positive function defined on some interval , satisfying a certain condition of limit. We prove that if is the sum of a convergent power series for with nonnegative coefficients and , then , where and depends only upon .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002993919880931724X
PII:
S 00029939(1988)0931724X
Keywords:
Power series,
HardyLittlewood theorem,
Weierstrass theorem,
moment sequence,
completely monotonic sequence
Article copyright:
© Copyright 1988
American Mathematical Society
