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Bloch functions and asymptotic tail variance | | Haakan Hedenmalm
; | | Date: |
22 Sep 2015 | | Abstract: | We obtain an optimal exponential square integrability theorem for the Bergman
projection of a function bounded by 1 in modulus. This is interpreted as the
statement that the asymptotic tail variance of such a function is at most 1.
The asymptotic tail variance defines a seminorm on the Bloch space. We apply
the main result to quasiconformal Teichm"uller theory, and obtain an estimate
of the integral means spectrum of k-quasiconformal mappings that are conformal
in the exterior disk: $B(k,t)lefrac14k^2|t|^2(1+7k)^2$. This is conjectured
asymptotically sharp as k tends to 0, by Prause and Smirnov (2011). | | Source: | arXiv, 1509.6630 | | Services: | Forum | Review | PDF | Favorites | |
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