The order of a linearly invariant family in Cn

Martin Chuaqui, Rodrigo Hernández

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Resumen

We study the (trace) order of the linearly invariant family in the ball Bn defined by {norm of matrix}SF{norm of matrix}≤α, where F:Bn→Cn is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of α and the dimension n. Lower bounds for the order are established in similar terms by means of examples.

Idioma originalInglés
Páginas (desde-hasta)372-379
Número de páginas8
PublicaciónJournal of Mathematical Analysis and Applications
Volumen398
N.º1
DOI
EstadoPublicada - 1 feb. 2013

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