A conjecture of L. Carleson and applications
Let $T_\alpha$ be the class of functions meromorphic in the unit disk ${\bf D}$ such that $$\int_D{|f'(z)|^2\over (1+|f(z)|^2)^2}(1-|z|)^{1-\alpha}dx\,dy<\infty,\quad 0\leq\alpha<1.$$ It is known that $T_\alpha\subset N$, where $N$ denotes the Nevanlinna class of functions meromorphic in $\bold D$ and of bounded characteristic. Because every $f\in N$ is a quotient of two bounded functions, analy
