Geodesic
Normal Functions: Lp Estimates
Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 55-73

Voir la notice de l'article provenant de la source Cambridge University Press

For ameromorphic (or harmonic) function ƒ, let us call the dilation of ƒ at z the ratio of the (spherical)metric at ƒ(z) and the (hyperbolic)metric at z. Inequalities are knownwhich estimate the sup norm of the dilation in terms of its Lp norm, for p > 2, while capitalizing on the symmetries of ƒ. In the present paper we weaken the hypothesis by showing that such estimates persist even if the Lp norms are taken only over the set of z on which ƒ 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.
DOI : 10.4153/CJM-1997-003-6
Mots-clés : 30D45, 30F35 
Chen, Huaihui; Gauthier, Paul M. Normal Functions: Lp Estimates. Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 55-73. doi: 10.4153/CJM-1997-003-6
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