Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bergman-type Singular Operators and the Characterization of Carleson
  Measures for Besov--Sobolev Spaces on the Complex Ball   The purposes of this paper are two fold. First, we extend the method of
non-homogeneous harmonic analysis of Nazarov, Treil and Volberg to handle
"Bergman--type" singular integral operators. The canonical example of such an
operator is the Beurling transform on the unit disc. Second, we use the methods
developed in this paper to settle the important open question about
characterizing the Carleson measures for the Besov--Sobolev space of analytic
functions $B^\sigma_2$ on the complex ball of $\mathbb{C}^d$. In particular, we
demonstrate that for any $\sigma> 0$, the Carleson measures for the space are
characterized by a "T1 Condition". The method of proof of these results is an
extension and another application of the work originated by Nazarov, Treil and
the first author.

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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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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: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph