M athematical I nequalities & A pplications Volume 7, Number 2 (2004), 199–205 GENERALIZATION OF HILBERT’S INTEGRAL INEQUALITY I. BRNETI ´ C AND J. PE ˇ CARI ´ C Abstract. A generalization of the well-known Hilbert’s inequality is given and several other results of this type obtained in the recent years follow as a special case from our result. Mathematics subject classification (2000): 26D15. Key words and phrases: Hilbert’s inequality, H¨ older’s inequality, Beta function, Gamma function. REFERENCES [1] BICHENG YANG, On Hilbert’s integral inequality, J. Math. Anal. Appl 220(1998) 778–785 [2] BICHENG YANG, On a General Hardy-Hilbert’s Integral Inequality, Chin. Ann. of Math. 21A(2000) 401–408 [3] BICHENG YANG, On an extension of Hardy-Hilbert’s Integral Inequality, Chin. Ann. of Math. 23A:2(2002) [4] T. C. PEACHEY, Some Integral Inequalities Related to Hilbert’s, Journal of Inequalities in Pure and Applied Mathematics, 4(1), Art.19 (2003) 1–8 [5] IOAN GAVREA, Some Remarks On Hilbert’s Integral Inequality, Mathematical Inequalities and Applica- tions, 5(3)(2002) 473–477 [6] YONG HONG, All-sided generalization about Hardy-Hilbert integral inequalities, Acta Mathematica Sinica, 44:4(2001) 619–626 c , Zagreb Paper MIA-07-22 Mathematical Inequalities & Applications www.ele-math.com mia@ele-math.com