Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for the complex Green operator: symmetry, percolation, and
  interpolation   Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of
$\mathbb{C}^{n}$ of hypersurface type. We show that Sobolev estimates for the
complex Green operator hold simultaneously for forms of symmetric bidegrees,
that is, they hold for $(p,q)$--forms if and only if they hold for
$(m-p,m-1-q)$--forms. Here $m$ equals the CR dimension of $M$ plus one.
Symmetries of this type are known to hold for compactness estimates. We further
show that with the usual microlocalization, compactness estimates for the
positive part percolate up the complex, i.e. if they hold for $(p,q)$--forms,
they also hold for $(p,q+1)$--forms. Similarly, compactness estimates for the
negative part percolate down the complex. As a result, if the complex Green
operator is compact on $(p,q_{1})$--forms and on $(p,q_{2})$--forms ($q_{1}\leq
q_{2}$), then it is compact on $(p,q)$--forms for $q_{1}\leq q\leq q_{2}$. It
is interesting to contrast this behavior of the complex Green operator with
that of the $\overline{\partial}$--Neumann operator on a pseudoconvex domain.

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The categories of this paper are: stat
3
The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
6
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: hep-lat
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The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
0
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: econ
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th