A strong form of Plessner's theorem
| Autor: | Gardiner, Stephen J., Manolaki, Myrto |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aim.2020.107489 |
| Popis: | Let $f$ be a holomorphic, or even meromorphic, function on the unit disc. Plessner's theorem then says that, for almost every boundary point $\zeta $, either (i) $f$ has a finite nontangential limit at $\zeta $, or (ii) the image $f(S)$ of any Stolz angle $S$ at $\zeta $ is dense in the complex plane. This paper shows that statement (ii) can be replaced by a much stronger assertion. This new theorem and its analogue for harmonic functions on halfspaces also strengthen classical results of Spencer, Stein and Carleson. Comment: In press, Advances in Mathematics (open access) |
| Databáze: | arXiv |
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