The talk is devoted to the study of necessary and sufficient topological conditions for an embedded real surfaceto lie in a strictly pseudoconvex domain on a complex surface. These results are used to construct Stein domains on algebraic manifolds and to describe envelopes of holomorphy of real surfaces in CP2 and in some other complex surfaces.
The problem of the realization of a Stein manifold fibered over a planar domain as a (fibered) subdomain of a linear space is discussed. An example of a 2-dimensional manifold fibered by discs but not equvialent to a subdomain of C2 is constructed.
This thesis deals with problems from two different fields of mathematics in the four included papers. The first two papers treat problems from harmonic analysis on Riemannian manifolds. Papers 3 and 4 give weighted estimates related to the $\bar\partial$ equation in several complex variables, and should be considered the main part of this thesis.