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A characterization of certain measures using quasiconformal mappings


Author: Craig A. Nolder
Journal: Proc. Amer. Math. Soc. 109 (1990), 349-356
MSC: Primary 30C60
DOI: https://doi.org/10.1090/S0002-9939-1990-1013976-2
MathSciNet review: 1013976
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Abstract: Suppose that $ \mu $ is a finite positive measure on the unit disk. Carleson showed that the $ {L^2}(\mu )$-norm is bounded by the $ {H^2}$-norm uniformly over the space of analytic functions on the unit disk if and only if $ \mu $ is a Carleson measure. Analogues of this result exist for Bergmann spaces of analytic functions in the disk and in the unit ball of $ {C^n}$. We prove here real variable analogues of certain Bergmann space results using quasiconformal and quasiregular mappings.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1013976-2
Keywords: Carleson measures, norm inequalities, quasiregular mappings
Article copyright: © Copyright 1990 American Mathematical Society

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