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Extreme points in spaces between Dirichlet and Vanishing Mean Oscillation

Published online by Cambridge University Press:  17 April 2009

K. J. Wirths  and
J. Xiao
K. J. Wirths
Affiliation:
Institute of Analysis, TU-Braunschweig, D-38106 Braunschweig, Germany, e-mail: kjwirths@tu-bs.de
J. Xiao
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada, e-mail: jxiao@math.mun.ca
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Abstract

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For p ∈ (0, ∞) define Qp0(∂Δ) as the space of all Lebesgue measurable complex-valued functions f; on the unit circle ∂Δ for which ∫∂Δf;(z)|dz|/(2π) = 0 and

as the open subarc I of ∂Δ varies. Note that each Qp,0(∂Δ) lies between the Dirichlet space and Sarason's vanishing mean oscillation space. This paper determines the extreme points of the closed unit ball of Qp,0(∂Δ) equipped with an appropriate norm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 365 - 375
Copyright
Copyright © Australian Mathematical Society 2003

References

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