Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An operator-valued T(1) theorem for symmetric singular integrals in UMD
  spaces   The natural BMO (bounded mean oscillation) conditions suggested by
scalar-valued results are known to be insufficient for the boundedness of
operator-valued paraproducts. Accordingly, the boundedness of operator-valued
singular integrals has only been available under versions of the classical
``$T(1)\in BMO$'' assumptions that are not easily checkable. Recently, Hong,
Liu and Mei (J. Funct. Anal. 2020) observed that the situation improves
remarkably for singular integrals with a symmetry assumption, so that a
classical $T(1)$ criterion still guarantees their $L^2$-boundedness on Hilbert
space -valued functions. Here, these results are extended to general UMD
(unconditional martingale differences) spaces with the same natural BMO
condition for symmetrised paraproducts, and requiring in addition only the
usual replacement of uniform bounds by $R$-bounds in the case of general
singular integrals. In particular, under these assumptions, we obtain
boundedness results on non-commutative $L^p$ spaces for all $1<p<\infty$,
without the need to replace the domain or the target by a related
non-commutative Hardy space as in the results of Hong et al. for $p\neq 2$.

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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex