Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity results for $\bar\partial_b$ on CR-manifolds of hypersurface
  type   We introduce a class of embedded CR manifolds satisfying a geometric
condition that we call weak $Y(q)$. For such manifolds, we show that dbar-b has
closed range on $L^2$ and that the complex Green operator is continuous on
$L^2$. Our methods involves building a weighted norm from a microlocal
decomposition. We also prove that at any Sobolev level there is a weight such
that the complex Green operator inverting the weighted Kohn Laplacian is
continuous. Thus, we can solve the dbar-b equation in $C^\infty$.

18
The categories of this paper are: econ
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga