/relax THE ANGULAR DISTRIBUTION OF MASS BY BERGMAN FUNCTIONS
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چکیده
Let D = {z : |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z : | arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0, then ∫ f−1(Σε) |f |dA > δ ∫
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تاریخ انتشار 1998