CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO QK SPACES

doi:10.1016/S0252-9602(09)60004-7

Abstract

Abstract:

The author gives a mild integral condition in a nondecreasing function K: [0, ∞) → [0, ∞), which is sufficient and the best possible to ensure that f is a Bloch function if and only if f belongs to Q_K, a Möbius-invariant space of functions
analytic in the unit disk. Their contributions are slight improvements of known results, and the proofs presented here are independently developed. The corresponding results for meromorphic case are also given.

Key words: Areally mean q-valent, circumferentially mean q-valent, Q_K spaces

CLC Number:

30D45

Hasi Wulan. CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO Q_K SPACES[J].Acta mathematica scientia,Series B, 2009, 29(1): 33-44.

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CRITERIA FOR AN ANALYTIC FUNCTION BELONGING TO Q_K SPACES

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