Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A weak notion of strict pseudo-convexity. Applications and examples   Let $\Omega $ be a bounded ${\mathcal{C}}^{\infty}$-smoothly bounded domain
in ${\mathbb{C}}^{n}.$ For such a domain we define a new notion between strict
pseudo-convexity and pseudo-convexity: the size of the set $W$ of weakly
pseudo-convex points on $\partial \Omega $ is small with respect to Minkowski
dimension: near each point in the boundary $\partial \Omega ,$ there is at
least one complex tangent direction in which the slices of $W$ has a upper
Minkowski dimension strictly smaller than $2.$ We propose to call this notion
"strong pseudo-convexity"; this word is free since "strict pseudo-convexity"
gets the precedence in the case where all the points in $\partial \Omega $ are
stricly pseudo-convex.
  For such domains we prove that if $S$ is a separated sequence of points
contained in the support of a divisor in the Blaschke class, then a canonical
measure associated to $S$ is bounded. If moreover the domain is $p$-regular,
and the sequence $S$ is dual bounded in the Hardy space $H^{p}(\Omega),$ then
the previous measure is Carleson.
  As an application we prove a theorem on interpolating sequences in bounded
convex domains of finte type in ${\mathbb{C}}^{n}.$
  Examples of such pseudo-convex domains are finite type domains in
${\mathbb{C}}^{2},$ finite type convex domains in ${\mathbb{C}}^{n},$ finite
type domains which have locally diagonalizable Levi form, domains with real
analytic boundary and of course, stricly pseudo-convex domains in
${\mathbb{C}}^{n}.$
  Domains like $|{z_{1}}| ^{2}+\exp \{1-|{z_{2}}| ^{-2}\}<1,$ which are not of
finite type are nevertheless strongly pseudo-convex, in this sense.

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The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an