The topics of this volume are diverse, but all of them are related to a huge area in analysis and applications where remarkably deep results and original approaches of Professor Maz'ya play a fundamental role. World-recognized experts present their new results covering, in particular, the following topics: Beurling's minimum principle, inverse hyperbolic problems, degenerate oblique derivative problems, the Lp-dissipativity connected with the Lp-contractivity of the generated semigroups, optimal control of a biharmonic obstacle problem sharp bilateral bounds of Green's function for the fractional Schrodinger operator, Bergman orthogonal polynomials, some class of singular integral operators, general Cwikel-Lieb-Rozenblum and Lieb-Thirring inequalities, the Laplace operator on domains with rough boundaries, integral and supremum operators, finite rank Toeplitz operators in the Bergman space, bounds on the resolvent of a non-selfadjoint pseudodifferential operator, the Faber-Krahn inequality, and some other topics.