Estimates of Pseudo-Differential Operators and Operator of Lipschitz Functions on Schatten Classes and von Neumann Norms

Abstract

We study the asymptotic distribution and singular values of compact pseudo differential operators. We determine the boundedness of a certain class and estimates for Schatten-von Neumann norms of Hardy-Steklov operators in lebesgue spaces. We give the bounds for constant in some operator inequalities in Schatten classes on compact manifolds, traces and global functional calculus for operators on compact Lie groups. We obtain the best constant in some non- commutative Martingle inequalities and for operator Lipschitz functions on Schatten classes. We estimate the approximation numbers of one class of integral operators. We show Wiener- Hopf operators on finite interval and the Schatten - von Neumann properties of some pseudodifferential operators. We establish the operator Lipschtiz functions and operator smoothness in Schatten -von Neumann classes and norms for functions of several variables.