2024/02/24 by Georgios Dosidis, Bae Jun Park, Dosidis, Georgios +3 · 3 citations
Mathematics · #42B15 #42B20 #42B25 #47H60 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2402.15785
openalex publication_date 2024/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish boundedness results for bilinear singular integral operators with rough homogeneous kernels whose restriction to the unit sphere belongs to the Orlicz space L(log L)α. This improves the previously best known condition for boundedness of such bilinear operators obtained in the paper of the first and third authors, and provides estimates close to the conjectured endpoint of integrability suggested by the linear theory. The proof is based on a new sharp boundedness criterion for bilinear Fourier multiplier operators associated with sums of dyadic dilations of a fixed symbol m0, compactly supported away from the origin. This criterion admits the best possible behavior with respect to a modulation of m0 and is intimately connected with sharp shifted square function estimates.