Academic Communication

Harmonic Analysis Techniques for the study of Partial Differential Equations2015-12-14

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Speaker:Prof. Han yongsheng

Time and Places:Dec 14, 21 14:00-16:00  Room 508, Teaching Building, West Third Ring Road North, Haidian District, Beijing, 100089 China.

                          Dec 16, 23 14:00-16:00,Room 314, No.4 Teaching Building, 105 West Third Ring Road North, Haidian District, Beijing, 100048 China.

                          Dec 18,25 14:00-16:00,Room 707, Teaching Building, 83 West Third Ring Road North, Haidian District, Beijing, 100089 China.

Organizer:School of Mathematical Sciences Capital Normal University

Introduction:Harmonic analysis methods have become of very powerful tools in the study of partial differential equations. Indeed, the classical theory of the first generation of Calder′ on-Zygmund operators played crucial roles in the study of elliptic and parabolic partial differential equations. Moreover, it was well known that the source of the theory of pseudo-differential operators is the second generation of Calderón-Zygmund operators. In particular, since the 1980s, the third generation of Calder′ on-Zygmund operators was established and provided key tools for solving many long standing open problems in partial differential equations.

The purpose of this series talks is to devoted to the presentation of a few basic harmonic analysis techniques which were often used in the study of partial differential equations. The main content of these talks is the following:

Chapter I:Calder’on-Zygmund singular integral operators

                 §1.1: Calder’on-Zygmund convolution operators;

                 §1.2:Riesz potentials

                 §1.3:Commutators;                               

                 §1.4:Paraproduct operators

Chapter II:Littlewood-Paley theory and function spaces

                 §2.1: BMO space;    

                 §2.2 :Besov space