Inequalities Against Equations?
Conference paper
First Online:
Abstract
The close connection between equations and inequalities will be illustrated on the example of the Hardy inequality.
Keywords
Friedrichs’ inequality Hardy’s inequality Sturm–Liouville problem spectral properties variational eigenvaluesPreview
Unable to display preview. Download preview PDF.
References
- 1.G.H. Hardy, J.E. Littlewood, G. Pόlya: Inequalities. Cambridge Univ. Press, 1934.Google Scholar
- 2.A. Kufner, L.E. Persson: Weighted Inequalities of Hardy Type. World Scientific, Singapore 2003.Google Scholar
- 3.P.R. Beesack: Hardy’s inequality and its extensions. Pacific J. Math. 11 (1961), 39–61.CrossRefMATHMathSciNetGoogle Scholar
- 4.G.A. Tomaselli: A class of inequalities. Boll. Un. Mat. Ital. (2) 22 (1969), 622–631.Google Scholar
- 5.B. Opic, A. Kufner: Hardy-Type Inequalities. Longman, Harlow 1990.Google Scholar
- 6.I.S. Kac, M.G. Krein: Criteria for discreteness of the spectra of a singular string. Izv. Vyss. Ucheb. Zaved. Mat. no 2 (1958), 136–153. (Russian)MathSciNetGoogle Scholar
- 7.P. Drábek, A. Kufner: Hardy inequality and properties of the quasilinear Sturm– Liouville problem. Atti. Accad. Naz. Lincei, Math. Appl. 18, no. 2 (2007), 125–138.Google Scholar
- 8.R.T. Lewis: The discreteness of the spectrum of self-adjoint, even order, one term, differential operators. Proc. Amer. Math. Soc. 42 (1974), 480–482.CrossRefMATHMathSciNetGoogle Scholar
Copyright information
© Springer Basel 2014