Coifman–Meyer multipliers: Leibniz-type rules and applications to scattering of solutions to PDEs
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- by Virginia Naibo and Alexander Thomson PDF
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Abstract:
Leibniz-type rules for Coifman–Meyer multiplier operators are studied in the settings of Triebel–Lizorkin and Besov spaces associated with 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 one 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.References
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Additional Information
- Virginia Naibo
- Affiliation: Department of Mathematics, Kansas State University, 138 Cardwell Hall, 1228 North 17th Street, Manhattan, Kansas 66506
- MR Author ID: 678614
- ORCID: 0000-0002-5440-6714
- Email: vnaibo@ksu.edu
- Alexander Thomson
- Affiliation: Department of Mathematics, Kansas State University, 138 Cardwell Hall, 1228 North 17th Street, Manhattan, Kansas 66506
- MR Author ID: 1083067
- Email: thomson521@ksu.edu
- Received by editor(s): April 8, 2018
- Received by editor(s) in revised form: September 27, 2018
- Published electronically: June 19, 2019
- Additional Notes: The authors were partially supported by the NSF under grant DMS 1500381.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 5453-5481
- MSC (2010): Primary 42B25, 42B15; Secondary 42B20, 46E35
- DOI: https://doi.org/10.1090/tran/7866
- MathSciNet review: 4014283