Results on meromorphic φ -normal functions

Let φ: [0, 1) → (0, ∞) be an increasing function. A meromorphic function f in the unit disc is said to be φ -normal if its spherical derivative f^#(z):=|f′(z)|/(1 +|f(z)|²) satisfies f^#(z) = O{script} (φ(|z|)) as |z| → 1^-. This article is devoted to the study of meromorphic φ-normal functions. In particular, an analogue of the Lohwater-Pommerenke theorem and several equivalent characterizations for φ-normal functions are established under certain regularity conditions on φ.