Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coifman-Meyer multipliers: Leibniz-type rules and applications to
  scattering of solutions to PDEs   Leibniz-type rules for Coifman-Meyer multiplier operators are studied in the
settings of Triebel-Lizorkin and Besov spaces associated to weights in the
Muckenhoupt classes. Even in the unweighted case, improvements on the currently
known estimates are obtained. The flexibility of the methods of proofs allows
to prove Leibniz-type rules in a variety of function spaces that include
Triebel-Lizorkin and Besov spaces based on weighted Lebesgue, Lorentz and
Morrey spaces as well as variable-exponent Lebesgue spaces. Applications to
scattering properties of solutions to certain systems of partial differential
equations involving fractional powers of the Laplacian are presented.

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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph