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On the extended Hilbert's inequality

Author(s): Gao Mingzhe; Yang Bichen
Journal: Proc. Amer. Math. Soc. 126 (1998), 751-759.
MSC (1991): Primary 26D15
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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:

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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