The basic properties of Bloch functions

[摘要] A Bloch functionf(z)is an analytic function on the unit disc?whose derivative grows no faster than a constant times the reciprocal of the distance fromzto∂?. We reprove here the basic analytic facts concerning Bloch functions. We establish the Banach space structure and collect facts concerning the geometry of the space. We indicate duality relationships, and known isomorphic correspondences are given. We give a rather complete list of references for further study in the case of several variables.

[学科分类] 数学（综合）