题    目：Difference Quotient Representation of Norms of Sobolev Spaces Associated with Ball Banach Function Spaces

主讲人：朱晨峰

单    位：浙江工业大学

时    间：2024年10月22日 10:00

地    点：数学与统计学院107教室

摘    要：In this talk, we will recall two celebrated formulae of Bourgain, Brezis & Mironescu and Maz’ya & Shaposhnikova, and two recent surprising formulae of Brezis, Seeger, Van Schaftingen & Yung and Gu & Yung, including their proofs and further generalizations. These formulae are related to fractional Sobolev spaces (Gagliardo semi-norm), first order Sobolev spaces, and (weak) Lebesgue spaces. Then we recall the concept of ball Banach function spaces and generalize the above four formulae to this setting; the counterparts on spaces of homogeneous type are also considered.

简    介：朱晨峰, 早年博士毕业于北京师范大学数学科学学院, 现为浙江工业大学数学科学学院博士后, 主要从事调和分析特别是函数空间实变理论及其应用的研究, 已在欧氏空间与齐型空间上的相关于球Banach函数空间的Sobolev空间, 抛物Muckenhoupt权类及其相关函数空间, 和Hardy-Lorentz空间的实变理论及其应用方面取得进展, 部分成果发表于Calc. Var. Partial Differential Equations, Commun. Contemp. Math.和J. Geom. Anal.等国际知名数学期刊上.