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

The class F consists of those functions with the property lim sup r → 1 − T ( r , f ) − log ( 1 − r ) = α ( f ) < + ∞ . Here we study the subclass S of F which consists of those functions in F with integrals not in F . In a sense the functions in S form a boundary for F in that all of their derivatives are in F , but any number of integrals of functions in S are not in F . We analyze the relationships between S and functions in Hardy, Bergman, and Dirichlet spaces. We also consider the power series representation of functions in S .