Function spaces and their operators

Linear operators on block matrices Lebesgue spaces and their properties: total boundedness, total positivity, estimates CB-norms. Generalizations of classical inequalities to matrix spaces. Asymptotics of the singular numbers of the simple layer type operators. Spectral asymptotics of the operator of fractional integration. Regularized traces of non-nuclear operators. Bergman projection. Bernstein type inequalities for entire functions. Membership of Blaschke products to Besov and Hardy-Sobolev spaces. Properties of the Libera operator. Area theorem for univalent functions. Convexity and starlikeness of univalent functions. Schwarz lemma, Lipschitz condition, and subharmonic behavior in the context of vector-valued analytic functions. BiBloch functions in the case of arbitrary weights. Quasiconformal mappings satisfying Poisson's equation. Spaces of polyharmonic functions. Besov and Hardy-Sobolev spaces of holomorphic functions on the ball. Composition operators. Coefficient multipliers.