分析和微分方程讨论班——Logvinenko-Sereda sets and Carleson measures on compact manifolds

报告人：王兴（湖南大学）

时间：2025年7月5日，11:00-12:00

地点：海纳苑2幢203室

摘要:Marzo and Ortega-Cerd`a gave geometric characterizations for L^p-Logvinenko-Sereda sets on the standard sphere. Later, Ortega-Cerd`a and Pridhnani further investigated L^2-Logvinenko-Sereda sets and L^2-Carleson measures on compact manifolds without boundary. In this paper, we  characterize L^p-Logvinenko-Sereda sets and L^p-Carleson measures on compact manifolds with or without boundary for all 1<p<\infty.   Furthermore, we investigate Logvinenko-Sereda sets and Carleson measures for eigenfunctions on compact manifolds without boundary, and we completely characterize them on the standard sphere for p > \frac{2m}{m-1}. For the range p < \frac{2m}{m-1}, we conjecture that L^p-Logvinenko-Sereda sets on the standard sphere are characterized by the tubular geometric control condition and we provide some evidence. These results provide new progress on an open problem raised  by Ortega-Cerd`a and Pridhnani.

联系人：席亚昆（yakunxi@zju.edu.cn）