Abstract
Suppose that μ \mu is a finite positive measure on the unit disk. Carleson showed that the L 2 ( μ ) {L^2}(\mu ) -norm is bounded by the H 2 {H^2} -norm uniformly over the space of analytic functions on the unit disk if and only if μ \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 {C^n} . We prove here real variable analogues of certain Bergmann space results using quasiconformal and quasiregular mappings.
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