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An extension of Calderon-Zygmund type singular integral

摘要:In this talk,  we  will present  a kind of singular integral which can be viewed as an extension of the classical Calderon-Zygmund type singular integral. We establish an estimate of the  singular integral in the  $L^q$ space for $1<q<\infty$. In particular, the  Calderon-Zygmund estimate can be recovered from our obtained estimate. The proof of our main result is via the so called "geometric approach". We will also present an application of this type singular integral in the approximation of surface quasi-geostrophic (SQG) equation.

个人简介:酒全森,首都师范大学数学科学学院教授,博士生导师,从事非线性偏微分方程、流体方程数学理论研究,在国际重要数学期刊上发表论文80余篇。在可压缩、不可压缩流体方程的解的适定性理论方面取得了多项国内外有影响的研究成果,被国内外权威学术刊物(如Comm. Math. Phys., Arch. Ration. Mech. Anal., SIAM J.Math. Anal.,等)接受发表。先后到香港中文大学数学研究所、美国普林斯顿大学、美国Oklahoma州立大学、法国萨瓦大学(Savoie University)等学术访问。于2003年获北京市“科技新星”计划(2003年),2013年获北京市“长城学者”计划。