一、报告题目:Fractional integration associated with multi-parameter dilations
二、报告人:王子鹏
三、时 间:2025 年 4 月 2 日 (周三)上午 10:00--11:00
四、地 点: 理学院A4-309
报告摘要:In this talk, we will first briefly review the history of fractional integrals and recall several classical results. Next, we introduce a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace. As a result, we give an extension of Stein-Weiss inequality to the multi-parameter setting. Lastly, we introduce a family of fractional integrals whose kernels satisfy Zygmund dilations. As a result, we obtain a Hardy-Littlewood-Sobolev type inequality.
报告人简介王子鹏,2015年于剑桥大学获得数学博士学位。自2012年7月起,同时在美国普林斯顿大学开始博士课题研究,师从调和分析大师 Elias M. Stein,并在其指导下完成博士论文。研究方向包括:1. 乘积空间上的分数次积分 (fractional integrals) 和傅立叶积分 (Fourier integrals);2. 分数次积分的离散形式。成果发表于Rev. Mat. Iberoam.、J. Differential Equations、Math. Proc. Cambridge Philos. Soc.、Studia Math.等期刊上。
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