A boundary property of some subclasses of functions of bounded type in the half-plane

Abstract

ABSTRACT: The paper gives the construction of the half-plane analog of the part of the factorization theory of M. M. Djrbashian – V. S. Zakaryan, where Djrbashian’s generalized fractional integral was used to establish the descriptive representations and boundary properties of meromorphic in the unit disc functions of the classes N{ω} contained in the Nevanlinna class N of functions of bounded type. Some results of nearly the same type are obtained for several weighted classes of meromorphic in the upper half-plane functions with bounded Tsuji characteristics by application of the Laplace transform along with an Hadamard–Liouville type generalized integro-differential operator with an unbounded integration contour, which becomes the Liouville integro-differentiation in a particular case.