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Hörmander's Carleson theorem for the ball

Published online by Cambridge University Press:  18 May 2009

S. C. Power
S. C. Power
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, U.S.A. Department of Mathematics, University of Lancaster, Bailrigg, Lancaster LA1 4YW, England
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Let denote the unit ball in ℂ2 and let Sdenote its boundary, the unit sphere. For z ∈ B and δ>0, the following non isotropic balls are defined, where

A finite positive Borel measure μ, on B is called a Carleson measure if there exists a constant C for which

Here σ denotes normalized surface area measure on S. The following theorem was obtained by Hörmander [6] as a special case of more general variants for strictly pseudoconvex domains in ℂn. Recently Cima and Wogen [3] derived it from a Carleson measure theorem for Bergman spaces of the ball. A different direct approach to the Bergman context, and related settings, is given in Leucking [7].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 13 - 17
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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