On some complex function spaces and classes (Q2758469)

The theory of complex function spaces and classes has been intensively studied during the last few decades. NEWLINENEWLINENEWLINEIn this interesting paper, the author studies analytic function spaces and meromorphic function classes. The paper is divided into the following sections. In Section 1 are introduced notations, terminology and definitions which are required for the forthcoming parts. In Sections 2 and 3 are studied precise relationships (in the sense of some strict set inclusions) between various analytic function spaces and meromorphic function classes. In Section 4 are deduced the main results which characterize the functions in \(F(p,q,s)\) and \(F_0(p,q,s)\) in terms of their \(n\)-th derivatives (Theorems 4.2.1-4.2.4). The results contained in Theorems 4.2.1 and 4.2.3 have applications to entire functions and Carleson measures. In Section 5 the author introduces two new families of function spaces. Finally (Section 6) the paper concludes with a number of interesting questions and open problems.