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2008 Some weighted sum and product inequalities in L^p spaces and their applications
R. C. Brown
Banach J. Math. Anal. 2(2): 42-58 (2008). DOI: 10.15352/bjma/1240336291


We survey some old and new results concerning weighted norm inequalities of sum and product form and apply the theory to obtain limit-point conditions for second order differential operators of Sturm-Liouville form defined in $L^p$ spaces. We also extend results of Anderson and Hinton by giving necessary and sufficient criteria that perturbations of such operators be relatively bounded. Our work is in part a generalization of the classical Hilbert space theory of Sturm-Liouville operators to a Banach space setting.


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R. C. Brown. "Some weighted sum and product inequalities in L^p spaces and their applications." Banach J. Math. Anal. 2 (2) 42 - 58, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1138.26010
MathSciNet: MR2404102
Digital Object Identifier: 10.15352/bjma/1240336291

Primary: 26D10
Secondary: 34B24 , 47A30 , 47E05

Keywords: limit-point conditions , relatively bounded perturbations , Sturm-Liouville operators , weighted product inequalities , weighted sum inequalities

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 2 • 2008
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