| On the Generalizations of Hilbert’s Inequality |
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| 作者姓名： | WANG Wen-jie~ HE Le-ping~ |
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| 作者单位： | 1.Department of Mathematics，Hunan University of Arts and Science，Changde 415000，China;2.College of Mathematics and Computer Science，Jishou University，Jishou 416000，China |
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| 摘 要： | 1 IntroductionLetan,bn>0.If 0<∑∞n=1a2n< ∞,0<∑∞n=1b2n< ∞,then∑∞m=1∑∞n=1ambnm n<π∑∞n=1a2n∑∞n=1b2n1/2(1)theinequality(1)is well knownintheliterature as Hilbert’sinequality.The associatedintegral formof(1)maybe writteninthe following:If 0<∫0∞f2(t)dt< ∞,0<∫0∞g2(t)dt< ∞,then∫0∫∞0∞f(xx) g(yy)dxdy<π∫(0∞f2(t)d∫t0∞g2(t)dt)1/2,(2)where the constantπare best possible in(1)and(2).In recent years,some i mprovements and extensions ofHilbert’s inequality have been given.Fori…
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On the Generalizations of Hilbert's Inequality |
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| WANG Wen-jie,HE Le-ping.On the Generalizations of Hilbert's Inequality[J].Journal of Xiangtan Normal University (Natural Science Edition),2006,28(3). |
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| Authors: | WANG Wen-jie HE Le-ping |
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| Institution: | 1. Department of Mathematics, Hunan University of Arts and Science,Changde 415000 , China
2. College of Mathematics and Computer Science, Jishou University,Jishou 416000, China |
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| Abstract: | In this paper, by employing a refined Cauchy's inequality, some strengthened Hilbert's inequality with parameter A, B,λ are further improved. |
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| Keywords: | Hilbert inequality Cauchy's inequality weight function beta function |
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