Arbre de Noël du GDR « Géométrie non-commutative »

Collection Arbre de Noël du GDR « Géométrie non-commutative »

Organizer(s) Amaury Freslon, Maria-Paula Gomez-Aparicio
Date(s) 01/12/2022 - 02/12/2022
linked URL
00:00:00 / 00:00:00
12 14

Schatten Properties of Commutators

By Kai Zeng

Given a quantum tori $\mathbb{T}_{\theta}^d$, we can define the Riesz transforms $\mathfrak{R}_j$ on the quantum tori and the commutator $đx_i$ := [$\mathfrak{R}_i,M_x$], where $M_x$ is the operator on $L^2(\mathbb{T}_{\theta}^d)$ of pointwise multiplication by $x \in L^\infty (\mathbb{T}_{\theta}^d)$. In this talk, we will characterize the Schatten properties of the commutator [$\mathfrak{R}_i,M_x$] by showing that $x \in B_{p,q}^{\alpha} ({\mathbb T}_{\theta}^d)$, where $B_{p,q}^{\alpha} ({\mathbb T}_{\theta}^d)$ is the Besov space on quantum tori. Futhermore, we will extend this characterisation to the more general case where $\mathfrak{R}_j$ replaced by an arbitrary Calderon-Zygmund operator. To date, these new results treat the quantum differentiability in the strictly noncommutative setting.

Information about the video

  • Date of recording 02/12/2022
  • Date of publication 04/12/2022
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4


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