A characterization of certain measures using quasiconformal mappings

Nolder, Craig A.

doi:10.1090/S0002-9939-1990-1013976-2

A characterization of certain measures using quasiconformal mappings
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Proc. Amer. Math. Soc. 109 (1990), 349-356 Request permission

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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