2019/02/27 by Pavel Zorin‐Kranich, Zorin-Kranich, Pavel
Mathematics · #42B20 (Primary) 42B25 #47A07 (Secondary) #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1902.10577
openalex publication_date 2019/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first three results in this thesis are motivated by a far-reaching conjecture on boundedness of singular Brascamp-Lieb forms. Firstly, we improve over the trivial estimate for their truncations, thus excluding potential trivial counterexamples. Secondly, in a dyadic model we give a partial result in the trilinear, 2-dimensional case when one of the functions depends only on one variable. Thirdly, we estimate the multidimensional version of the polynomial Carleson operator, whose boundedness would also be a consequence of the conejcture. The final pair of results concerns directional square functions. One of them concerns interaction of Lipschitz change of variable on the line with Littlewood--Paley decomposition and is used to extend the conditional result of Lacey and Li for Hilbert transform along C1+ε vector fields to Lipschitz vector fields. The other concerns directional averaging operators and gives an alternative approach to a single scale maximal function with averages in N directions due to Katz away from the endpoint.