Abstract
In this paper, we will prove a matrix weighted T1 theorem regarding the boundedness of certain matrix kernelled CZOs on matrix weighted $$L^p(W)$$ for matrix A $${}_p$$ weights W. Using some of the ideas from the proof, we will also establish a natural matrix weighted John–Nirenberg result that extends to the matrix setting (in the case when one of the weights is the identity) a very recent characterization of both S. Bloom’s BMO space and the two weight boundedness of commutators by I. Holmes, M. Lacey, and B. Wick.
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