Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A direct proof of Sobolev embeddings for quasi-homogeneous
  Lizorkin--Triebel spaces with mixed norms   The article deals with a simplified proof of the Sobolev embedding theorem
for Lizorkin--Triebel spaces (that contain the $L_p$-Sobolev spaces $H^s_p$ as
special cases). The method extends to a proof of the corresponding fact for
general Lizorkin--Triebel spaces based on mixed $L_p$-norms. In this context a
Nikol'skij--Plancherel--Polya inequality for sequences of functions satisfying
a geometric rectangle condition is proved. The results extend also to spaces of
the quasi-homogeneous type.

0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
16
The categories of this paper are: stat
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics