Banach Journal of Mathematical Analysis

Some weighted sum and product inequalities in L^p spaces and their applications

R. C. Brown

Full-text: Open access

Abstract

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.

Article information

Source
Banach J. Math. Anal., Volume 2, Number 2 (2008), 42-58.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240336291

Digital Object Identifier
doi:10.15352/bjma/1240336291

Mathematical Reviews number (MathSciNet)
MR2404102

Zentralblatt MATH identifier
1138.26010

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 47A30: Norms (inequalities, more than one norm, etc.) 34B24: Sturm-Liouville theory [See also 34Lxx] 47E05: Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)

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

Citation

Brown, R. C. Some weighted sum and product inequalities in L^p spaces and their applications. Banach J. Math. Anal. 2 (2008), no. 2, 42--58. doi:10.15352/bjma/1240336291. https://projecteuclid.org/euclid.bjma/1240336291


Export citation