Carleson's theorem
Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emer...
| Autor: | |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2034 |
| Acceso en línea: | https://ddd.uab.cat/record/2034 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_48204_01 |
| Access Level: | acceso abierto |
| Palabra clave: | Pointwise convergence Fourier series Singular integrals Phase plane analysis |
| Sumario: | Carleson's Theorem from 1965 states that the partial Fourier sums of a square integrable function converge pointwise. We prove an equivalent statement on the real line, following the method developed by the author and C. Thiele. This theorem, and the proof presented, is at the center of an emerging theory which complements the statement and proof of Carleson's theorem. An outline of these variations is also given. |
|---|