Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local regularity of the Green operator in a CR manifold of general
  "type"   It is here proved that if a pseudoconvex CR manifold $M$ of hypersurface type
has a certain "type", that we quantify by a vanishing rate $F$ at a submanifold
of CR dimension $0$, then $\Box_b$ "gains $f^2$ derivatives" where $f$ is
defined by inversion of $F$. Indeed the estimate is more accurate and it
involves the Levi form of $M$ and of additional weights, instead of $\Box_b$.
Next a general tangential estimate, "twisted" by a pseudodifferential operator
$\Psi$ is established. The combination of the two yields a general
"$f$-estimate" twisted by $\Psi$. We apply the twisted estimate for $\Psi$
which is the composition of a cut-off $\eta$ with a differentiation of order
$s$ such as $R^s$ of Section 4. Under the assumption that $[\partial_b,\eta]$
and $[\partial_b,[\bar\partial_b,\eta]]$ are superlogarithmic multipliers in a
sense inspired to Kohn, we get the local regularity of the Green operator
$G=\Box_b^{-1}$. In particular, if $M$ has "infraexponential type" along
$S\setminus\Gamma$ where $S$ is a manifold of CR dimension $0$ and $\Gamma$ a
curve transversal to $T^{\mathbb C} M$, then we have local regularity of $G$.
This gives an immediate proof of former work by Baracco, Khanh, Zampieri and by
Kohn. The conclusion extends to "block decomposed" domains for whose blocks the
above hypotheses hold separately. In the application of Section 4, $\Psi$ is
composed by a cut off $\eta$ and a differentiation of order $s$ such as
$\Lambda^s$ or $R^s$ and $M$ is a decoupled hypersurface which has
infraexponential type along the coordinate lines $\mathbb
R_{x_j}\setminus\{0\}$ and whose equations have differentials which are
superlogarithmic multipliers in the sense of Kohn. In this situation, $\Box_b$
is locally hypoelliptic.

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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs