Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bilipschitz maps, analytic capacity, and the Cauchy integral   Let vphi:C rightarrow C be a bilipschitz map. We prove that if E\subset\C is
compact, and gamma(E), alpha(E) stand for its analytic and continuous analytic
capacity respectively, then C^{-1}\gamma(E)\leq \gamma(\vphi(E)) \leq
C\gamma(E) and C^{-1}\alpha(E)\leq \alpha(\vphi(E)) \leq C\alpha(E), where C
depends only on the bilipschitz constant of vphi. Further, we show that if mu
is a Radon measure on C and the Cauchy transform is bounded on L^2(\mu), then
the Cauchy transform is also bounded on L^2(\vphi_\sharp\mu), where
vphi_\sharp\mu is the image measure of mu by vphi. To obtain these results, we
estimate the curvature of vphi_\sharp\mu by means of a corona type
decomposition.

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The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas