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Carleson measures and conformal self-mappings in the real unit ball

✍ Scribed by Marko Kotilainen; Visa Latvala; Jouni Rättyä

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
126 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Bounded and compact Carleson measures in the unit ball Bof R^n^ , n ≥ 2, are characterized by means of global Dirichlet integrals of the conformal self‐map T~a~ taking a ∈ B to the origin. The same proof applies in the unit ball of C^n^ . It is also proved that the powers of the Jacobian of T~a~ satisfy the weak Harnack inequality and even Harnack's inequality with a constant independent of a. As an application of these results it is shown that the two different definitions for Carleson measures in the existing literature are equivalent for a certain range of parameter values. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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