Univalent functions and Dirichlet-Morrey spaces

Higher Schwarzian derivative and Dirichlet Morrey space

“…We will prove this Lemma by using mathematical induction. It follows from Corollary 2.5 in [24] that if µ ∈ M(D * ), then σ 3 ( f µ )(z) ∈ N pλ,3 . Now suppose that σ n ( f µ ) ∈ N pλ,n , n ≥ 3, we shall prove that…”

“…Theorem 1.2. [24] Suppose that f is a bounded univalent function in D and log f ∈ B 0 , 0 < λ < 1 and 0 < p ≤ 1.…”