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arXiv · 1702.04569

The sharp square function estimate with matrix weight

Tuomas Hytönen·Stefanie Petermichl·Alexander Volberg
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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.

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Tuomas Hytönen, Stefanie Petermichl, Alexander Volberg. 2019-03-30. The sharp square function estimate with matrix weight. https://doi.org/10.19086/da.7597

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