Optimal Lifting of Levi-degenerate Hypersurfaces and Applications to the Cauchy--Szegö Projection
강병찬
129동 309호
0
3156
06.11 16:51
| 구분 | 조화해석학 |
|---|---|
| 일정 | 2026-06-25(목) 16:00~17:00 |
| 세미나실 | 129동 309호 |
| 강연자 | Ji Li (Macquarie University) |
| 담당교수 | 이상혁 |
| 기타 |
Abstract: We will discuss a geometric lifting theorem for a Levi-degenerate hypersurface that lacks a group structure, specifically focusing on the Nagel–Stein polynomial model do-main.
Because the original boundary has no global Lie group law compatible with its horizontal vector fields, we introduce an optimized lifting to a stratified nilpotent Lie group.
This construction yields exactly left-invariant vector fields without Rothschild-Stein error terms, which allows us to push down a group Taylor expansion directly onto the original hypersurface.
As a primary application, we present a sharp Schatten class theorem for commutators of the Cauchy–Szegö projection. We demonstrate that for p > 4, the commutator belongs to the Schatten class Sp if and only if the symbol is in the Besov space Bp.
Furthermore, we establish a rigidity theorem for 0 < p ≤ 4, showing that the commutator belongs to Sp if and only if the symbol is constant.
This reveals that the critical Schatten index is 4, independent of the degree of degeneracy, which is governed by the lower-dimensional behavior of the degenerate geometry.
