The sharp square function estimate with matrix weight

Abstract

We prove the matrix $A_2$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear dependence on the matrix $A_2$ constant in the estimate. Moreover, we give a mixed estimate in terms of $A_2$ and $A_{\infty }$ constants. Key is a sparse domination of a process inspired by the integrated form of the matrix--weighted square function.

Published Version

References in corpus (1)

• On pointwise estimates involving sparse operators

Cited by in corpus (7)

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• Sparse Domination for Bi-Parameter Operators Using Square Functions
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• Weighted estimates of the Bergman projection with matrix weights
• Mixed $A_2$-$A_{\infty }$ estimates of the non-homogeneous vector square function with matrix weights
• Sharp bounds and T1 theorem for Calderón-Zygmund operators with matrix kernel on matrix weighted spaces
• A matrix weighted bilinear Carleson Lemma and Maximal Function