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On the $ L^\infty\times L^\infty\rightarrow BMO$ mapping property for certain bilinear pseudodifferential operators


Author: Virginia Naibo
Journal: Proc. Amer. Math. Soc. 143 (2015), 5323-5336
MSC (2010): Primary 35S05, 47G30; Secondary 42B20, 42B35
DOI: https://doi.org/10.1090/proc12775
Published electronically: June 10, 2015
MathSciNet review: 3411149
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Abstract: Boundedness from $ L^\infty \times L^\infty $ into $ BMO$ is proved for bilinear pseudodifferential operators with symbols in a range of bilinear Hörmander classes of critical order. This is achieved by means of new continuity results for bilinear operators with symbols in certain classes and a new pointwise inequality relating bilinear operators and maximal functions.


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Additional Information

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

DOI: https://doi.org/10.1090/proc12775
Keywords: Bilinear pseudodifferential operators, H\"ormander classes, critical order, BMO
Received by editor(s): October 5, 2014
Published electronically: June 10, 2015
Additional Notes: This work was partially supported by NSF under grant DMS 1101327.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society

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