Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol

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Abstract

We are going to show that the commutator of the Hilbert transform with matrix multiplication by a BMO matrix of size n×n is bounded by a multiple of logn times the BMO-norm of the matrix.

Résumé

Nous allons démontrer une majoration de la forme ‖HB−BH‖L2(Cn)→L2(Cn)≤Clogn‖B‖BMO pour une fonction matricielle B de BMO.

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