On a boundary version of Morera's theorem.
On an Estimate of Axler and Shapiro.
On boundary behaviour of Bergman kernel function for plane domains and their Cartesian products
On horospheres and holomorphic endomorfisms of the Siegel disc
On propagation of boundary continuity of holomorphic functions of several variables
We prove that continuity properties of bounded analytic functions in bounded smoothly bounded pseudoconvex domains in two-dimensional affine space are determined by their behaviour near the Shilov boundary. Namely, if the function has continuous extension to an open subset of the boundary containing the Shilov boundary it extends continuously to the whole boundary. If it is e.g. Hölder continuous on such a boundary set, it is Hölder continuous on the closure of the domain. The statements may fail...
On the existence of bounded holomorphic functions on complete Kähler manifolds.