Séminaire Analyse Harmonique
Classes of Singular Integral Operators and Applications to Boundary Value Problems
17
March 2026
March 2026
| Intervenant : | Dorina Mitrea |
| Institution : | Baylor University (Texas, USA) |
| Heure : | 14h00 - 15h00 |
| Lieu : | Bâtiment 307, salle 2L8 |
A. P. Calderón and A. Zygmund have been at the forefront of a program aimed at developing a theory for singular integral operators as a means for treating problems in partial differential equations. Initially formulated in ${\mathbb{R}}^n$, the theory has evolved to the point of now accommodating the most general geometric setting in which singular integral operators are bounded on Lebesgue spaces namely, uniformly rectifiable sets.
In this talk, I will survey some of the most recent advances, with special emphasis on categorizing subclasses of singular integral operators which are well behaved on various scales of spaces of interest. These include (boundary) Sobolev spaces, Hölder spaces, spaces of functions with bounded mean oscillations, spaces of functions with vanishing mean oscillations, Orlicz spaces, Muckenhoupt weighted Lebesgue spaces, and Morrey spaces.