Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sup-norm Estimates for $\overline{\partial}$ in $\mathbb{C}^3$   We develop a method for proving sup-norm and H\"older estimates for
$\overline{\partial}$ on wide class of finite type pseudoconvex domains in
$\mathbb{C}^n$. A fundamental obstruction to proving sup-norm estimates is the
possibility of singular complex curves with exceptionally high order of contact
with the boundary. Our method handles this problem, and in $\mathbb{C}^3$, we
prove sup-norm and H\"older estimates for all bounded, pseudoconvex domains
with real-analytic boundary.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
18
The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: cond-mat