On characteristic of bounded analytic functions involving hyperbolic derivative

In this article, we give the Nevanlinna type hyperbolic characteristics in simply connected domains and angular domains and the Tsuji type hyperbolic characteristics for bounded analytic functions for the first time. The first fundamental theorems are also established concerning hyperbolic derivative for bounded analytic functions in simply connected domains and angular domains. This is a continuous work of Makhmutov [3].

A strengthened Schwarz-pick inequality for derivatives of the hyperbolic metric

This paper is to investigate the Schwarz-Pick inequality for the hyperbolic derivative. Our result is not only a contraction but also a contraction minus a positive constant and this improves Beardon's theorem greatly.

Fractional integration and the hyperbolic derivative

We improve S. Yamashita's hyperbolic version of the well-known Hardy-Littlewood theorem. Let f be holomorphic and bounded by one in the unit disc D. If (f#)p has a harmonic mojorant in D for some p, p > 0, then so does σ(f)q for all q, 0 < q < ∞. Here