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Bilinear operators with homogeneous symbols, smooth molecules, and Kato-Ponce inequalities


Authors: Joshua Brummer and Virginia Naibo
Journal: Proc. Amer. Math. Soc. 146 (2018), 1217-1230
MSC (2010): Primary 47G30, 42B35; Secondary 46E35
DOI: https://doi.org/10.1090/proc/13841
Published electronically: October 5, 2017
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Abstract: We present a unifying approach to establish mapping properties for bilinear pseudodifferential operators with homogeneous symbols in the settings of function spaces that admit a discrete transform and molecular decompositions in the sense of Frazier and Jawerth. As an application, we obtain related Kato-Ponce inequalities.


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Additional Information

Joshua Brummer
Affiliation: Department of Mathematics, Kansas State University, 138 Cardwell Hall, 1228 N. 17th Street, Manhattan, Kansas 66506
Email: brummerjd@math.ksu.edu

Virginia Naibo
Affiliation: Department of Mathematics, Kansas State University, 138 Cardwell Hall, 1228 N. 17th Street, Manhattan, Kansas 66506
Email: vnaibo@math.ksu.edu

DOI: https://doi.org/10.1090/proc/13841
Keywords: Pseudodifferential operators, homogeneous symbols, smooth molecules, Kato-Ponce inequalities.
Received by editor(s): December 14, 2016
Received by editor(s) in revised form: May 5, 2017
Published electronically: October 5, 2017
Additional Notes: The authors were partially supported by the NSF under grant DMS 1500381.
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2017 American Mathematical Society

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