Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric conditions for the $L^2$-boundedness of singular integral
  operators with odd kernels with respect to measures with polynomial growth in
  $\mathbb{R}^d$   Let $\mu$ be a finite Radon measure in $\mathbb{R}^d$ with polynomial growth
of degree $n$, although not necessarily $n$-AD-regular. We prove that under
some geometric conditions on $\mu$ that are closely related to rectifiability
and involve the so-called $\beta$-numbers of Jones, David and Semmes, all
singular integral operators with an odd and sufficiently smooth
Calder\'on-Zygmund kernel are bounded in $L^2(\mu)$. As a corollary, we obtain
a lower bound for the Lipschitz harmonic capacity of a compact set in
$\mathbb{R}^d$ only in terms of its metric and geometric properties.

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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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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: supr-con
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom