Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilinear operator-valued Calder\'on-Zygmund theory   We develop a general theory of multilinear singular integrals with
operator-valued kernels, acting on tuples of UMD Banach spaces. This, in
particular, involves investigating multilinear variants of the $\mathcal
R$-boundedness condition naturally arising in operator-valued theory. We
proceed by establishing a suitable representation of multilinear,
operator-valued singular integrals in terms of operator-valued dyadic shifts
and paraproducts, and studying the boundedness of these model operators via
dyadic-probabilistic Banach space-valued analysis. In the bilinear case, we
obtain a $T(1)$-type theorem without any additional assumptions on the Banach
spaces other than the necessary UMD. Higher degrees of multilinearity are
tackled via a new formulation of the Rademacher maximal function (RMF)
condition. In addition to the natural UMD lattice cases, our RMF condition
covers suitable tuples of non-commutative $L^p$-spaces. We employ our
operator-valued theory to obtain new multilinear, multi-parameter,
operator-valued theorems in the natural setting of UMD spaces with property
$\alpha$.

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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex