The basic properties of Bloch functions
A Bloch function f(z) is an analytic function on the unit disc 𝔻 whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂𝔻. We reprove here the basic analytic facts concerning Bloch functions. We establish the Banach space structure and collect facts concerni...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
1979-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000314 |
| Summary: | A Bloch function f(z) is an analytic function on the unit disc 𝔻 whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂𝔻. 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |