Estimates for truncated area functionals on the Bloch space
Recently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n ≤ 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n = 6. We p...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/710052 |
| Acceso en línea: | http://hdl.handle.net/10486/710052 https://dx.doi.org/10.1090/proc/16382 |
| Access Level: | acceso abierto |
| Palabra clave: | Bloch Functions Bloch Space Coefficient Problems Unit Disk Coefficient Matemáticas |
| Sumario: | Recently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n ≤ 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n = 6. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all n. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of 4/e). We also consider related weighted estimates for functionals involving the powers nt, t > 0, and show that the exponent t = 1 represents the critical case for the expected sharp estimate |
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