A class of meromorphic functions of slow growth in the unit disk not containing any of their integrals

[摘要] The class consists of those functions with the property lim sup T(r,f)/r -> 1(-) -log(1 - r) = alpha(f) < + infinity. Here we study the subclass 4 of which consists of those functions in Y with integrals not in F. In a sense the functions in 4 form a boundary for Y in that all of their derivatives are in F, but any number of integrals of functions in 4 are not in Y. We analyze the relationships between 4 and functions in Hardy, Bergman, and Dirichlet spaces. We also consider the power series representation of functions in 4. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Nevanlinna characteristic;Analytic in the unit disk;Class F;Value distribution