Abstract
In this paper, the following sharp estimate is proved:
where F is the conformal mapping of the domain \(D^ - = \left\{ {\zeta :\left| \zeta \right| > 1} \right\}\) onto the exterior of a convex curve, with \(F\prime \left( \infty \right) = 1\). For p=1, this result is due to Pólya and Shiffer. We also obtain several generalizations of this estimate under other geometric assumptions about the structure of the domain F(D -).
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Kayumov, I.R. Sharp Estimates for Integral Means for Three Classes of Domains. Mathematical Notes 76, 472–477 (2004). https://doi.org/10.1023/B:MATN.0000043477.92354.86
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DOI: https://doi.org/10.1023/B:MATN.0000043477.92354.86