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For 0<p<∞,  Qp#  (Qp,0#) is the class of meromorphic functions f defined in the unit disk D={z:|z|<1} satisfying sup⁡w∈D∬D(f#(z))2gp(z,w)dσz<∞  (lim⁡w→∂D∬D(f#(z))2gp(z,w)dσz=0), where g(z,w) is Green's function of D. Criteria for funtions f to belong to Qp#  (Qp,0#) are given by the Ahlfors-Shimizu characteristic. Further, outer functions in Qp#  (Qp,0#) are characterized and shown that every function in Qp#  (Qp,0#) can be represented as the quotient of two functions in H∞∩Qp#  (H∞∩Qp,0#)

journal of function spaces and applications/journal of function spaces and applications

Outer functions in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mo>#</mml:mo></mml:mrow></mml:msubsup><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>#</mml:mo></mml:mrow></mml:msubsup></mml:math>

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