On a class of quasiconformal functions in Banach spaces

Abstract:

A quasiconformal function f on a domain D in a complex Banach space E is defined as a function on D such that for every holomorphic mapping $\Phi$ from the unit disk $\Delta$ into D the composite mapping $f \circ \Phi$ is quasiconformal in the usual sense. With respect to the Kobayashi-Kiernan pseudo distance on D, Schwarz’s lemma, Liouville’s theorem and the little Picard theorem are obtained for quasiconformal functions. A maximum modulus principle is also obtained for quasiconformal functions.