For p≤1 and A_p matrix weights, matrix-weighted Hardy spaces admit maximal-function, atomic, finite-atomic, and Calderón–Zygmund operator characterizations.
New Characterizations and Properties of Matrix $A_\infty$ Weights
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We provide several new characterizations of $A_{p,\infty}$-matrix weights, originally introduced by A. Volberg as matrix-valued substitutes of the classical $A_\infty$ weights. In analogy with the notion of $A_p$-dimension of matrix weights introduced in our previous work, we introduce the concepts of the lower and the upper dimensions of $A_{p,\infty}$-matrix weights, which enable us to obtain sharp estimates related to their reducing operators. In a follow-up work, these results will play a key role in the study of function spaces with $A_{p,\infty}$-matrix weights, which extends earlier results in the more restricted class of $A_p$-matrix weights.
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Maximal Function and Atomic Characterizations of Matrix-Weighted Hardy Spaces with Their Applications to Boundedness of Calder\'on--Zygmund Operators
For p≤1 and A_p matrix weights, matrix-weighted Hardy spaces admit maximal-function, atomic, finite-atomic, and Calderón–Zygmund operator characterizations.