On the Differentiability of T(r,f)
International Journal of Mathematics and Mathematical Sciences
It is well known that T(r,f) is differentiable at least for r>r0. We show that, in fact, T(r,f) is differentiable for all but at most one value of r, and if T(r,f) fails to have a derivative for some value of r, then f is a constant times a quotient of finite Blaschke products.
Douglas W. Townsend (1982).
On the Differentiability of T(r,f). International Journal of Mathematics and Mathematical Sciences.5 (2), 351-356.