Abstract
Let h1, h2 and h3 be continuous functions from the unit disk double-struck D sign into the Riemann sphere ℂ such that hi(z) ≠ hj(z) (i ≠ j) for each z ∈ double-struck D sign. We prove that the set ℱ of all functions f meromorphic on double-struck D sign such that f(z) ≠ hj(z) for all z ∈ D and j = 1, 2, 3 is a normal family. The result and the method of the proof extend to quasimeromorphic functions in higher dimensions as well.
Original language | English (US) |
---|---|
Pages (from-to) | 379-387 |
Number of pages | 9 |
Journal | Journal d'Analyse Mathematique |
Volume | 79 |
DOIs | |
State | Published - 1999 |
ASJC Scopus subject areas
- Analysis
- Mathematics(all)