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Several regularity estimates in harmonic analysis and PDEs

Li Chen (Aarhus University)
Tuesday 6 February 2024 14:15–15:30 Aud. D3 (1531-215)
Mathematics Seminar

Heat semigroups lie at the interface of analysis, PDEs, probability and geometry. Heat semigroup techniques have important applications in the study of regularity estimates in harmonic analysis and PDEs. In this talk, we first discuss regularisation properties of heat semigroups and their applications in functional inequalities and Riesz transforms in different geometric settings. Then we study boundary value problems for degenerate elliptic operators where off-diagonal heat semigroup estimates play a crucial role. Finally, we also discuss sharp and dimension-free bounds of singular integral operators via the martingale transform method.

Organised by: SBiM
Contact: Jan Frahm Revised: 31.01.2024