Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary
  Carleson Curves   In 1968, Israel Gohberg and Naum Krupnik discovered that local spectra of
singular integral operators with piecewise continuous coefficients on Lebesgue
spaces $L^p(\Gamma)$ over Lyapunov curves have the shape of circular arcs.
About 25 years later, Albrecht B\"ottcher and Yuri Karlovich realized that
these circular arcs metamorphose to so-called logarithmic leaves with a median
separating point when Lyapunov curves metamorphose to arbitrary Carleson
curves. We show that this result remains valid in a more general setting of
variable Lebesgue spaces $L^{p(\cdot)}(\Gamma)$ where $p:\Gamma\to(1,\infty)$
satisfies the Dini-Lipschitz condition. One of the main ingredients of the
proof is a new sufficient condition for the boundedness of the Cauchy singular
integral operator on variable Lebesgue spaces with weights related to
oscillations of Carleson curves.

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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics