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On the coefficients of functions with bounded boundary rotation

1972
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Proceedings of the American Mathematical Society
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Let Vk be the class of normalised functions of bounded boundary rotation. For/6 Vt define M(r,f) = max |/(z)|, |s|_r and let L(r,f) denote the length of/(|z|=r). Then if/(z)=z+ 2n=2anz", it is shown that (i) 2M(r,f)<L(r,f)^knM(r,f), and (ii) n-\at\-^{T¡k\rn-'í)M(r,f'), n^.2. The class At of meromorphic functions of boundary rotation is also studied and estimates for the coefficients are given.

doi:10.1090/s0002-9939-1972-0308384-2
fatcat:7hkbth274batbjj44nex5v7324