1. CJM 2011 (vol 63 pp. 862)
2. CJM 1998 (vol 50 pp. 449)
3. CJM 1997 (vol 49 pp. 55)
 Chen, Huaihui; Gauthier, Paul M.

Normal Functions: $L^p$ Estimates
For a meromorphic (or harmonic) function $f$, let us call the dilation
of $f$ at $z$ the ratio of the (spherical) metric at $f(z)$ and the
(hyperbolic) metric at $z$. Inequalities are known which estimate
the $\sup$ norm of the dilation in terms of its $L^p$ norm, for $p>2$,
while capitalizing on the symmetries of $f$. In the present paper
we weaken the hypothesis by showing that such estimates persist
even if the $L^p$ norms are taken only over the set of $z$ on which
$f$ takes values in a fixed spherical disk. Naturally, the bigger
the disk, the better the estimate. Also, We give estimates for
holomorphic functions without zeros and for harmonic functions in
the case that $p=2$.
Categories:30D45, 30F35 
