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It is shown that a univalent function f belongs to QK if and only if sup a∈∫01M∞2(r,f∘φa-f(a))K′(log (1/r))dr<∞, where φa(z)=(a-z)/(1-a¯z), provided K satisfies certain regularity conditions. It is also shown that under these conditions QK contains all univalent Bloch functions if and only if ∫01(log ((1+r)/(1-r)))2K′(log (1/r))dr<∞

abstract and applied analysis

Univalent Functions in the Möbius Invariant<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mi>Q</mml:mi><mml:mi>K</mml:mi></mml:msub></mml:mrow></mml:math>Space

Univalent Functions in the Möbius InvariantQKSpace