2024/06/03 by Wei Wang, Wang, Wei, Qingyan Wu +1 · 1 citation
Mathematics · Medicine · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #Dupuytren's Contracture and Treatments #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2406.01453
openalex publication_date 2024/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Cauchy-Szegö singular integral is a fundamental tool in the study of holomorphic Hp Hardy space. But for a kind of Siegel domains, the Cauchy-Szegö kernels are neither product ones nor flag ones on the Shilov boundaries, which have the structure of nilpotent Lie groups \mathscr N of step two. We use the lifting method to investigate flag-like singular integrals on \mathscr N , which includes these Cauchy-Szegö ones as a special case. The lifting group is the product \mathscr N of three Heisenberg groups, and naturally geometric or analytical objects on \mathscr N are the projection of those on \mathscr N . As in the flag case, we introduce various notions on \mathscr N adapted to geometric feature of these kernels, such as tubes, nontangential regions, tube maximal functions, Littlewood-Paley functions, tents, shards and atoms etc. They have the feature of tri-parameters, although the second step of the group \mathscr N is only 2-dimensional, i.e. there exists a hidden parameter as in the flag case. We also establish the corresponding Calderón reproducing formula, characterization of L p (\mathscr N) by Littlewood-Paley functions, L p -boundedness of tube maximal functions and flag-like singular integrals and atomic decomposition of H1 Hardy space on \mathscr N .