H 2 Of commutators and Jacobians

Auteurs : Hytönen, Tuomas P. (Auteur de la Conférence)
CIRM (Editeur )

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​Jacobian equation ​Iwaniec conjecture ​Ahlfors-Beurling operator ​commutator theorem ​bounded mean oscillation ​Lerner's formula randomisation ​questions from the audience

Résumé : The boundedness (on $L^p$ spaces) of commutators $[b,T] = bT-Tb$ of pointwise multiplication $b$ and singular integral operators $T$ has been well studied for a long time. Curiously, the necessary conditions for this boundedness to happen are generally less understood than the sufficient conditions, for instance what comes to the assumptions on the operator $T$. I will discuss some new results in this direction, and show how this circle of ideas relates to the mapping properties of the Jacobian (the determinant of the derivative matrix) on first order Sobolev spaces. This is work in progress at the time of submitting the abstract, so I will hopefully be able to present some fairly fresh material.

Codes MSC :
42B20 - Singular and oscillatory integrals, several variables
42B35 - Function spaces arising in harmonic analysis

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 26/04/2018
    Date de captation : 24/04/2018
    Sous collection : Research talks
    arXiv category : Analysis of PDEs ; Complex Variables ; Functional Analysis
    Domaine : Analysis and its Applications ; PDE
    Format : MP4 (.mp4) - HD
    Durée : 01:05:01
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2018-04-24_Hytonen.mp4

Informations sur la rencontre

Nom de la rencontre : Harmonic analysis of elliptic and parabolic partial differential equations / Analyse harmonique des équations aux dérivées partielles elliptiques et paraboliques
Organisateurs de la rencontre : Monniaux, Sylvie ; Portal, Pierre
Dates : 23/04/2018 - 27/04/2018
Année de la rencontre : 2018
URL Congrès : https://conferences.cirm-math.fr/1741.html

Citation Data

DOI : 10.24350/CIRM.V.19398203
Cite this video as: Hytönen, Tuomas P. (2018). Of commutators and Jacobians. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19398203
URI : http://dx.doi.org/10.24350/CIRM.V.19398203

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