题    目：Ponce-type Compactness Theorem for Sobolev Spaces Associated with Ball Banach Function Spaces

主讲人：林孝盛  讲师

单    位：集美大学

时    间：2026年6月10日  10:00

腾讯ID：739-729-130

密    码：681049

摘    要：The aim of this talk is to present a Ponce-type compactness theorem for Sobolev spaces associated with ball Banach function spaces on bounded Lipschitz domains. This result partly extends the compactness theorem of Ponce in [J. Eur. Math. Soc. 6 (2004), 1--15]. Unlike Ponce's original proof, our argument relies on a new decomposition of bounded Lipschitz domains and weighted fractional Poincar\'e inequalities on the corresponding local pieces. As applications, we obtain fractional Poincar\'e inequalities in this general function space setting and use them to prove the well-posedness of a weighted Triebel--Lizorkin type nonlocal variational problem. This talk is based on joint work with Dachun Yang, Wen Yuan, and Yangyang Zhang.

简    介：林孝盛, 2025年博士毕业于北京师范大学数学科学学院, 现为集美大学讲师. 主要从事调和分析及其应用的研究, 相关成果发表于 《J. Funct. Anal.》、《Calc. Var. Partial Differential Equations》和 《Constr. Approx.》等知名数学期刊上.