We prove the following extension of one direction in Marty's theorem: If k is a natural number, α > 1 and F is a family of functions meromorphic on a domain D all of whose poles have multiplicity at least k/α-1, then the normality of F implies that the family (Formula presented.) is locally uniformly bounded.
Bibliographical noteFunding Information:
Research of Shahar Nevo was supported by the Israel Science Foundation, Grant No. 395/2007.
- Marty's theorem
- Nevanlinna theory
- Normal families