Harmonic Measure, L 2 Estimates and the Schwarzian Derivative
نویسندگان
چکیده
Abstrac t . We consider several results, each o f which uses some type o f " L 2' ' es t imate to provide information about harmonic measure on planar domains. The first gives an a.e. characterization of tangent points o f a curve in terms of a certain geometric square function. Our next result is an LP est imate relating the derivative of a conformal mapping to its Schwarzian derivative. One consequence of this is an est imate on harmonic measure ~eneralizing Lavrent iev 's est imate for rectifiable domains. Finally, we consider L z es t imates for Schwarzian derivatives and the quest ion of when a Riemann mapping ~ has log ~ in BMO.
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تاریخ انتشار 1994