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...

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Detalles Bibliográficos
Autor: Lacey, Michael T.
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
Descripción
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.