Explore the Schatten properties of commutators in quantum tori during this 43-minute lecture by Kai Zeng from Université de Bourgogne-Franche-Comté at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the characterization of Schatten properties for the commutator [$\mathfrak{R}_i,M_x$] on quantum tori $\mathbb{T}_{\theta}^d$, where $\mathfrak{R}_j$ represents Riesz transforms and $M_x$ is the pointwise multiplication operator. Discover how these properties relate to Besov spaces $B_{p,q}^{\alpha} ({\mathbb T}_{\theta}^d)$ on quantum tori. Examine the extension of this characterization to cases involving arbitrary Calderon-Zygmund operators. Gain insights into quantum differentiability in strictly noncommutative settings through these new results.
Schatten Properties of Commutators on Quantum Tori
Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Overview
Syllabus
Kai Zeng - Schatten Properties of Commutators
Taught by
Institut des Hautes Etudes Scientifiques (IHES)