Carleson conditions for weights: The quantitative small constant case
We investigate the small constant case of a characterization of A∞ weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarithm of the A∞ constant by the Carleson norm of a measure built out of the heat extension, up to a multiplicative and additive cons...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2072/484449 |
| Acceso en línea: | http://hdl.handle.net/2072/484449 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary value problems Carleson measures Elliptic measure Muckenhoupt weights Perturabations 51 |
| Sumario: | We investigate the small constant case of a characterization of A∞ weights due to Fefferman, Kenig and Pipher. In their work, Fefferman, Kenig and Pipher bound the logarithm of the A∞ constant by the Carleson norm of a measure built out of the heat extension, up to a multiplicative and additive constant (as well as the converse). We prove, qualitatively, that when one of these quantities is small, then so is the other. In fact, we show that these quantities are bounded by a constant times the square root of the other, provided at least one of them is sufficiently small. We also give an application of our result to the study of elliptic measures associated to elliptic operators with coefficients satisfying the “Dahlberg–Kenig–Pipher” condition. |
|---|