勷勤数学•专家报告

题      目：Singular Integrals and Hardy Spaces Associated with Para-Accretive Functions in the Dunkl Setting

报  告  人：韩永生 教授  (邀请人：韩彦昌)

                                     奥本大学

时      间： 12月18日  15：00-16:00

地     点：数科院东楼304

报告人简介:

       韩永生教授是国际上知名的调和分析专家。美国奥本大学终身教授。本科毕业于北京大学，博士毕业于华盛顿大学师从于著名的数学家G.Weiss。 近四十年来致力于调和分析和函空间的理论研究。近年来已在国际主流的学术刊物上（Memoirs of ams, JFA, Math.Z,Transaction of ams等）发表论文100余篇。多次应邀在国际国内的重要的数学大会上作报告。

摘      要：

         In 1984, David, Journé, and Semmes established the celebrated T1 theorem, which provided a necessary and sufficient condition for the L2-boundedness of general Calderón–Zygmund operators Despite its broad applicability, this theorem does not extend to proving the L2-boundedness of the Cauchy integral on Lipschitz curves.

         A function b is called accretive if b,b^-1∈L2 and  Re(b) ≥ c > 0 a.e.. Subsequently, Coifman, McIntosh, and Meyer developed the so-called Tb theorem. As a key application, this theorem confirms the L2-boundedness of the Cauchy integral on Lipschitz curves.

      Later, David, Journé, and Semmes generalized this result to para-accretive functions b, which satisfy the following conditions:

b,b-1∈L∞ and  for all cube  with  for some 0