On Conformal Mapping^of Regions Bounded by Smooth Curves

An explicit expression in terms of these parameters is obtained for AP. The fact that the integral in (3) remains bounded for 0^p<l under the assumption that C has continuously turning tangents was proved in an earlier paper of the writer [4, p. 362 j.1 The emphasis in the present note is upon the fact that the constant Ap depends only on the parameters indicated and is expressed explicitly in terms of these quantities. This result is of use when an estimate for the integral in (3) is desired which holds uniformly for the mapping functions of a family of curves C.