Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev inequalities and the d-bar-Neumann operator   We study a complex valued version of the Sobolev inequalities and its
relationship to compactness of the d-bar-Neumann operator. For this purpose we
use an abstract characterization of compactness derived from a general
description of precompact subsets in L^2-spaces. Finally we remark that the
d-bar-Neumann operator can be continuously extended provided a subelliptic
estimate holds.

18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat