Isoperimetric inequalities for Bergman analytic content
| Autor: | Gardiner, Stephen J., Ghergu, Marius, Sjödin, Tomas |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| Popis: | The Bergman $p$-analytic content ($1\leq p<\infty $) of a planar domain $\Omega $ measures the $L^{p}(\Omega )$-distance between $\overline{z}$ and the Bergman space $A^{p}(\Omega )$ of holomorphic functions. It has a natural analogue in all dimensions which is formulated in terms of harmonic vector fields. This paper investigates isoperimetric inequalities for Bergman $p$-analytic content in terms of the St Venant functional for torsional rigidity, and addresses the cases of equality with the upper and lower bounds. Comment: 18 pages. To appear in Indiana University Mathematics Journal |
| Databáze: | arXiv |
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