On the coefficients of functions with bounded boundary rotation

D. K. Thomas
1972 Proceedings of the American Mathematical Society  
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