Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sobolev and Schatten Estimates for the Complex Green Operator on Spheres   The complex Green operator $\mathcal{G}$ on CR manifolds is the inverse of
the Kohn-Laplacian $\square_b$ on the orthogonal complement of its kernel. In
this note, we prove Schatten and Sobolev estimates for $\mathcal{G}$ on the
unit sphere $\mathbb{S}^{2n-1}\subset \mathbb{C}^n$. We obtain these estimates
by using the spectrum of $\square_b$ and the asymptotics of the eigenvalues of
the usual Laplace-Beltrami operator.

31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex