Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L^3 estimates for an algebraic variable coefficient Wolff circular
  maximal function   In 1997, Thomas Wolff proved sharp $L^3$ bounds for his circular maximal
function, and in 1999, Kolasa and Wolff proved certain non-sharp $L^p$
inequalities for a broader class of maximal functions arising from curves of
the form $\{\Phi(x,\cdot)=r\}$, where $\Phi(x,y)$ satisfied Sogge's cinematic
curvature condition. Under the additional hypothesis that $\Phi$ is algebraic,
we obtain a sharp $L^3$ bound on the corresponding maximal function. Since the
function $\Phi(x,y)=|x-y|$ is algebraic and satisfies the cinematic curvature
condition, our result generalizes Wolff's $L^3$ bound. The algebraicity
condition allows us to employ the techniques of vertical cell decompositions
and random sampling, which have been extensively developed in the computational
geometry literature.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int