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...
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| Format: | Article |
| Language: | English |
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Wiley
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000314 |
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| _version_ | 1850158311644594176 |
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| author | Joseph A. Cima |
| author_facet | Joseph A. Cima |
| author_sort | Joseph A. Cima |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-67fb9542e87549f68952f29df2c65935 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-67fb9542e87549f68952f29df2c659352025-08-20T02:23:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012336941310.1155/S0161171279000314The basic properties of Bloch functionsJoseph A. Cima0Mathematics Department, The University of North Carolina at Chapel Hill, Chapel Hill 27514, North Carolina, USAA 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.http://dx.doi.org/10.1155/S0161171279000314Bloch functionschlicht discsnormal functionsisomorphic Banah spacesMobius invariant subspaces. |
| spellingShingle | Joseph A. Cima The basic properties of Bloch functions International Journal of Mathematics and Mathematical Sciences Bloch function schlicht discs normal functions isomorphic Banah spaces Mobius invariant subspaces. |
| title | The basic properties of Bloch functions |
| title_full | The basic properties of Bloch functions |
| title_fullStr | The basic properties of Bloch functions |
| title_full_unstemmed | The basic properties of Bloch functions |
| title_short | The basic properties of Bloch functions |
| title_sort | basic properties of bloch functions |
| topic | Bloch function schlicht discs normal functions isomorphic Banah spaces Mobius invariant subspaces. |
| url | http://dx.doi.org/10.1155/S0161171279000314 |
| work_keys_str_mv | AT josephacima thebasicpropertiesofblochfunctions AT josephacima basicpropertiesofblochfunctions |