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On the extended Hilbert's inequality


Authors: Gao Mingzhe and Yang Bichen
Journal: Proc. Amer. Math. Soc. 126 (1998), 751-759
MSC (1991): Primary 26D15
DOI: https://doi.org/10.1090/S0002-9939-98-04444-X
MathSciNet review: 1459122
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Abstract: In this paper, it is shown that the extended Hilbert's inequality for double series can be refined by the aid of the Euler-Maclaurin summation formula. The extreme cases $p\rightarrow 1^+$ and $q\rightarrow+\infty$ are discussed.


References [Enhancements On Off] (What's this?)

  • 1. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, 1952. MR 13:727e
  • 2. D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, 1970. MR 43:448
  • 3. Gao Mingzhe, An improvement of Hardy-Riesz's Extension of the Hilbert Inequality, J. Math. Res. Exposition, Vol. 14, No. 2 (1994). MR 95m:26040
  • 4. Zhao Dejun, On a Refinement of Hilbert's Double Series Theorem, Math. In Practice and Theory, Beijin, China.

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Additional Information

Gao Mingzhe
Affiliation: Department of Mathematics, Xiangxi Education College for Nationalities, Jishou, Hunan 416000, People’s Republic of China

Yang Bichen
Affiliation: Department of Mathematics, Guangdong College of Education, Guangzhou 510303, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-98-04444-X
Keywords: Double series, infimum, Euler-Maclaurin summation formula
Received by editor(s): December 6, 1995
Received by editor(s) in revised form: August 29, 1996
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1998 American Mathematical Society

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