Let be a Lipschitz function. If is a bounded self-adjoint operator and if are commuting bounded self-adjoint operators such that then
where is a constant independent of , and and denotes the weak -norm.
If (respectively, ) are commuting bounded self-adjoint operators such that then
Soit une fonction Lipschitzienne. Si est un opérateur borné auto-adjoint et si sont des opérateurs bornés auto-adjoints qui commutent et tels que alors
où est une constante indépendante de , et et désigne la norme -faible.
Si (respectivement ) sont des opérateurs bornés qui commutent et tels que alors
Revised:
Accepted:
Published online:
Keywords: Non-commutative $L_p$-spaces, commutator estimates, Calderón–Zygmund theory
Mot clés : Espaces $L_p$ non commutatifs, estimées de commutateurs, théorie de Calderón–Zygmund
@article{AIF_2018__68_4_1643_0, author = {Caspers, Martijn and Sukochev, Fedor and Zanin, Dmitriy}, title = {Weak type operator {Lipschitz} and commutator estimates for commuting tuples}, journal = {Annales de l'Institut Fourier}, pages = {1643--1669}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {4}, year = {2018}, doi = {10.5802/aif.3195}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3195/} }
TY - JOUR AU - Caspers, Martijn AU - Sukochev, Fedor AU - Zanin, Dmitriy TI - Weak type operator Lipschitz and commutator estimates for commuting tuples JO - Annales de l'Institut Fourier PY - 2018 SP - 1643 EP - 1669 VL - 68 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3195/ DO - 10.5802/aif.3195 LA - en ID - AIF_2018__68_4_1643_0 ER -
%0 Journal Article %A Caspers, Martijn %A Sukochev, Fedor %A Zanin, Dmitriy %T Weak type operator Lipschitz and commutator estimates for commuting tuples %J Annales de l'Institut Fourier %D 2018 %P 1643-1669 %V 68 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3195/ %R 10.5802/aif.3195 %G en %F AIF_2018__68_4_1643_0
Caspers, Martijn; Sukochev, Fedor; Zanin, Dmitriy. Weak type operator Lipschitz and commutator estimates for commuting tuples. Annales de l'Institut Fourier, Volume 68 (2018) no. 4, pp. 1643-1669. doi : 10.5802/aif.3195. http://archive.numdam.org/articles/10.5802/aif.3195/
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