A boundary property of some subclasses of functions of bounded type in the half-plane (2017)
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 Nω 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.