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A property of univalent functions inA_{p}

Published online by Cambridge University Press:  07 August 2001

David Walsh
David Walsh
Affiliation:
Department of Mathematics, NUI Maynooth, Co. Kildare, Ireland
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Abstract

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The univalent functions in the diagonal Besov space A_{p}, where 1<p<\infty , are characterized in terms of the distance from the boundary of a point in the image domain. Here A_{2} is the Dirichlet space. A consequence is that there exist functions in A_{p},\ p>2, for which the area of the complement of the image of the unit disc is zero.

1991 Mathematics Subject Classification 30C99, 46E35.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 1 , March 2000 , pp. 121 - 124
Copyright
2000 Glasgow Mathematical Journal Trust