Home > On Trace Inequalities and Compactness for Potential-Type Operators
Thesis Info
Access Option
Author
Usman Ashraf
Supervisor
Alexander Meskhi
Program
PhD
Institute
Government College University
City
Lahore
Province
Punjab
Country
Pakistan
Thesis Completing Year
2008
Thesis Completion Status
Completed
Subject
Mathemaics
Language
English
Link
http://prr.hec.gov.pk/jspui/handle/123456789/263
Added
2021-02-17 19:49:13
Modified
2024-03-24 20:25:49
ARI ID
1676726809851
Similar
Necessary and sufficient conditions on a weight function v guaranteeing the bounded- ness/compactness of the Riemann-Liouville transform with variable parameter R α(x) q(x) from L p(x) to L v are found. The measure of non-compactness of this operation is also estimated from both sides in variable exponent spaces. Necessary and sufficient conditions guaranteeing the trace inequality for positive kernel operators in classical Lebesgue spaces defined on cones of nilpotent groups are established. Compactness criteria for these operators in classical weighted Lebesgue spaces are also obtained. Two-sided estimate for Schatten-von Neumann ideal norms of weighted higher order kernel operators are established. Asymptotic formulas for singular numbers for some potential-type operators are derived. Some of these results are applied to the problem of the existence of non-negative solution for certain non- linear integral equation.
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