Some Classes of Meromorphic Functions Characterized by Their Spherical Derivative

The Yosida Class is Universal

“…Remark. The second inequality was proved by Gavrilov [5] for the class Y 0,−1 (which he denoted W 0 1 ). Proof.…”

“…Yosida [17] has shown that given f ∈ A 0 and ǫ > 0 there exists some δ > 0, such that |z−h|<ǫ f # (z) d(x, y) > δ holds for every h ∈ C. The analog for Y α,β is Theorem 2 below. For β fixed, |h| > 1 and ǫ > 0 we set (5) ∆ ǫ (h) = {z : |z − h| < ǫ|h| −β }.…”

On the growth of meromorphic solutions of the Schwarzian differential equations

“…The distribution of values of functions in W 1 and W 2 has been thoroughly investigated by Julia [10], Yosida [19] and Ostrowski [17]. Gavrilov [5] and Makhmutov [15,16] have made a substantial contribution to the study of W p . Lemma 1 [16].…”