Abstract
The Hardy integral inequality is one of the most important inequalities in analysis. The present paper establishes some new Copson-Pachpatte (C-P) type inequalities, which are the generalizations of the Hardy integral inequalities on binary functions.
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Hardy, G. H. Note on a theorem of Hilbert. Math. Z., 6, 314–317 (1920)
Hardy, G. H., Littlewood, J. E., and Polya, G. Inequalities, Cambridge University Press, Cambridge (1934)
Hardy, G. H. Notes on some points in the integral calculus. Messenger of Mathematics, 57, 12–16 (1928)
Pachpatte, B. G. On some generalizations of Hardy’s integral inequality. J. Math. Anal. Appl., 234, 15–30 (1999)
Pachpatte, B. G. A note on certain inequalities related to Hardy’s inequality. Indian J. Pure Appl. Math., 23, 773–776 (1992)
Pecaric, J. E. and Love, E. R. Still more generalizations of Hardy’s inequality. J. Austral. Math. Soc., 58, 1–11 (1995)
Love, E. R. Generalizations of Hardy’s inequality. Proc. Roy. Soc. Edinburgh, Sect. A, 100, 237–262 (1985)
Yang, B. C. On Hardy-Hilbert’s integral inequality. J. Math. Anal. Appl., 261, 295–306 (2001)
Kuang, J. C. and Debnath, L. On new generalizations of Hilbert’s inequality and their applications. J. Math. Anal. Appl., 245, 248–265 (2000)
Wedestig, A. Some new Hardy type inequalities and their limiting inequalities. J. Ineq. Pure Appl. Math., 4, Article 61 (2003)
Zhao, C. and Debnath, L. Some new inverse type Hilbert integral inequalities. J. Math. Anal. Appl., 262, 411–418 (2001)
Miklyukov, V. M. and Vuorinen, M. K. Hardy’s inequality for W 1,p0 -functions on Riemannian manifolds. Proc. Amer. Math. Soc., 127, 2745–2754 (1999)
Opic, B. and Kufner, A. Hardy-Type Inequalities, Longman, Essex, England (1990)
Kufner, A. and Persson, L. E. Weighted Inequalities of Hardy Type, World Scientific, Singapore (2003)
Copson, E. T. Some integral inequalities. Proc. Roy. Soc. Edinburgh, Sect. A, 75, 157–164 (1975)
Izumi, M. and Izumi, S. On some inequalities for Fourier series. J. Anal. Math., 21, 277–291 (1968)
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Project supported by the National Basic Research Program of China (No. 2011CB302402) and the National Natural Science Foundation of China (No. 11171053)
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Leng, T., Feng, Y. On Hardy-type integral inequalities. Appl. Math. Mech.-Engl. Ed. 34, 1297–1304 (2013). https://doi.org/10.1007/s10483-013-1746-x
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DOI: https://doi.org/10.1007/s10483-013-1746-x