走向现代数学学术报告 - 杨大春教授（No. 692）

报告题目：Ball Banach Function Spaces Meet BBM, BVY, and BSVY Formulae

报告人：杨大春 教授（北京师范大学）

报告时间：2024年4月17日 16:30

报告地点：东海岸校区-D实209

报告摘要：The concept of ball quasi-Banach function (BQBF) spaces was introduced in 2017 by Y. Sawano, K.-P. Ho, D. Yang, and S. Yang. It is well known that some well-known function spaces, such as Morrey spaces, weighted Lebesgue spaces, mixed-norm Lebesgue spaces, and Orlicz-slice spaces, are ball quasi-Banach function spaces, but not quasi-Banach function spaces. In this talk, we will first recall the celebrated ({\bf BBM}) formulae of J. Bourgain, H. Brezis, and P. Mironescu and the recent surprising ({\bf BVY} and {\bf BSVY}) formulae of H. Brezis, A. Seeger, J. Van Schaftingen, and P.-L. Yung. Then we will introduce some recent extensions of these formulae to Sobolev spaces associated with ball Banach function spaces. In particular, we will introduce some methods on how to overcome the difficulties caused by the deficiency of the translation invariance, the rotation invariance, and the explicit expression of the quasi-norm of BQBF spaces under consideration.

报告人简介：杨大春教授现为北京师范大学博士生导师，二级教授，中共中央统战部联系的党外专家，第八届教育部科学技术委员会数理学部委员和北京师范大学第八届学术委员会委员。杨大春教授主要从事基础数学调和分析特别是函数空间实变理论及其应用方面的工作, 在欧氏空间和度量测度空间等底空间上的各种函数空间实变理论获得了一系列优秀成果，已承担多项国家自然科学基金及教育部博士点基金项目， 2006年被评为北京市优秀教师，目前是教育部和科技部“基础数学调和分析及其应用创新引智基地”项目负责人。