Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The factorizations of $H^\rho(\mathbb{R}^n)$ via multilinear
  Calder\'{o}n-Zygmund operators on weighted Lebesgue spaces   We extend the recently much-studied Hardy factorization theorems to the
weight case. The key point of this paper is to establish the factorization
theorems without individual condition on the weight functions. As a direct
application, we obtain the characterizations of $BMO(\mathbb{R}^n)$ space and
Lipschitz spaces via the weighted boundedness of commutators of multilinear
Calder\'{o}n-Zygmund operators with the genuinely multilinear weights.

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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th