Hishchak T. Boundary properties of functions in Hardy-type spaces

In Chapter 1 we introduce an overview of works related to Hardy spaces and formulate the main results of the thesis.In Chapter 2 of the dissertation paper we consider relationships between properties of functions in Hardy-type spaces and the behavior of functions inside the domain of analyticity. We obtain existence theorems and uniqueness theorems in weighted Hardy spaces. In Chapter 3 the description of the translation invariant subspaces of weighted Hardy spaces is supplemented. We showed the equivalence of the rapid growth in some sense on imaginary axis and rapid decrease on the positive half-axis for functions in Hardy-type spaces.We describe the properties of the space defined by the intersections of weighted Hardy spaces.In Chapter 3 for the decomposition problem in Paley-Wiener space we found the new way of splitting.