Skip navigation

상단메뉴

글로벌메뉴

좌측메뉴

학술행사

검색

Seminars

Seminar
FIELD Math:Analysis
DATE January 11 (Mon), 2021
TIME 15:00-16:30
PLACE 8101
SPEAKER Lee, Sanghyuk
HOST Jeong, In-Jee
INSTITUTE 서울대학교
TITLE Sharp $L^p-L^q$ estimates for the Hermite spectral projection
ABSTRACT This talk primarily concerns the sharp bound on the spectral projection of the Hermite operator in the $L^p$ spaces. In comparison with the spectral projection of the Laplacian, the sharp bound is not so well understood. We consider the estimate for the spectral Hermite projection in general $L^p-L^q$ framework and obtain various new sharp estimates in an extended range. Especially, we provide a complete characterization of the local estimate and prove the endpoint $L^2$--$L^{2(d+3)/(d+1)}$ estimate which has been left open since the work of Koch and Tataru. We also discuss application of the projection estimate to related problems, such as the resolvent estimate for the Hermite operator and Carleman estimate for the heat operator.
FILE  
  • list

date

~