Carleson's Theorem: Proof, Complements, Variations

By Michael T. Lacey. 2003

49 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/6b7502f855ebc45893d6beb7cdf1e9c2289fb365

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In Applied Mathematics

1. Kristian Seip
2. Christoph Aistleitner
3. István Berkes
4. Andriy V. Bondarenko
5. Chun-Kit Lai

Citations in the corpus

• GCD sums from Poisson integrals and systems of dilated functions (2012, background): “and difficult result with several astonishing consequences (see e.g. Lemma 3 below); for a comprehensive presentation of Carleson’s theorem, we refer to the monographs [3, 26] and to the survey article [23]. Gapoˇshkin [14] observed that as a direct consequence of Carleson’s theorem, (9) also implies ”