The Bi-Carleson operator

2004/09/21 by Camil Muscalu, Terence Tao, Muscalu, Camil +3 · 1 citation
Mathematics · #42A20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.CA #msc:42A20

paper · pdf · doi:10.48550/arxiv.math/0409406

44 pages, 3 figures, to appear, GAFA. This is the final version, incorporating referee suggestions

openalex publication_date 2004/09/21 · arxiv created 2005/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove L^p estimates for the Bi-Carleson operator, which is a natural hybrid of the Carleson maximal operator and the bilinear Hilbert transform. The methods used are essentially based on the treatment of the Walsh analogue of the operator in the prequel of this paper, but with additional technicalities due to the fact that in the Fourier model one cannot obtain perfect localization in both space and frequency.

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