Pakistan Research Repository

On Trace Inequalities and Compactness for Potential Type Operators

Ashraf, Usman (2009) On Trace Inequalities and Compactness for Potential Type Operators. PhD thesis, Govt. College University, Lahore .



Necessary and sufficient conditions on a weight function v guaranteeing the boundedness/compactness of the Riemann-Liouville transform with variable parameter R(x) from Lp(x) to Lq(x)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 de ned 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 nonlinear integral equation.

Item Type:Thesis (PhD)
Uncontrolled Keywords:Trace, Inequalities, Compactness, Potential, Type. Operators, weight, function, nilpotent, groups, Asymptotic, formulas
Subjects:Physical Sciences (f) > Mathematics(f5)
ID Code:6351
Deposited By:Mr. Javed Memon
Deposited On:30 Jun 2011 12:27
Last Modified:30 Jun 2011 12:27

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