Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-Localized Operators on Matrix Weighted $L^2$ Spaces   Nazarov-Treil-Volberg recently proved an elegant two-weight T1 theorem for
"almost diagonal" operators that played a key role in the proof of the $A_2$
conjecture for dyadic shifts and related operators. In this paper, we obtain a
generalization of their T1 theorem to the setting of matrix weights. Our
theorem does differ slightly from the scalar results, a fact attributable
almost completely to differences between the scalar and matrix Carleson
Embedding Theorems. The main tools include a reduction to the study of
well-localized operators, a new system of Haar functions adapted to matrix
weights, and a matrix Carleson Embedding Theorem.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn