Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domains of pseudo-differential operators: a case for the
  Triebel--Lizorkin spaces   The main result is that every pseudo-differential operator of type 1,1 and
order $d$ is continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$,
$1\le p<\infty$, and that this is optimal within the Besov and
Triebel--Lizorkin scales.The proof also leads to the known continuity for
$s>d$, while for all real $s$ the sufficiency of H\"ormander's condition on the
twisted diagonal is carried over to the Besov and Triebel--Lizorkin framework.
To obtain this, type 1,1-operators are extended to distributions with compact
spectrum, and Fourier transformed operators of this type are on such
distributions proved to satisfy a support rule, generalising the rule for
convolutions. Thereby the use of reduced symbols, as introduced by Coifman and
Meyer, is replaced by direct application of the paradifferential methods. A few
flaws in the literature have been detected and corrected.

24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat