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Maximal Function and Atomic Characterizations of Matrix-Weighted Hardy Spaces with Their Applications to Boundedness of Calder\'on--Zygmund Operators
Let $p\in(0,1]$ and $W$ be an $A_p$-matrix weight, which in scalar case is exactly a Muckenhoupt $A_1$ weight. In this article, we introduce matrix-weighted Hardy spaces $H^p_W$ via the matrix-weighted grand non-tangential maximal function and characterize them, respectively, in terms of various other maximal functions and atoms, both of which …