Title of Thesis
On Trace Inequalities and Compactness for Potential Type
Abdus Salam School of Mathematical Sciences / GC
|Number of Pages|
|Keywords (Extracted from title, table of contents and
abstract of thesis)|
Trace, Inequalities, Compactness,
Potential, Type. Operators, weight, function, nilpotent, groups,
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.