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Commutator estimates for Hölder continuous and bmo-Sobolev multipliers


Author: Michael E. Taylor
Journal: Proc. Amer. Math. Soc. 143 (2015), 5265-5274
MSC (2010): Primary 42B20, 42B25, 42B35, 35S05, 35S50
DOI: https://doi.org/10.1090/proc/12825
Published electronically: July 15, 2015
MathSciNet review: 3411144
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Abstract: We discuss conditions on a function $ f$ under which the commutator $ [P,f]$ of a pseudodifferential operator $ P$ of order $ m$ with the operation of multiplication by $ f$ is an operator of order $ m-r$ on various function spaces, namely Hölder-Zygmund spaces and $ L^p$-Sobolev spaces, given $ 0<r<1$. We also establish an endpoint case involving $ r=1$, and we extend the scope to all $ r>0$ for a particularly significant case in 1 dimension.


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Additional Information

Michael E. Taylor
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599

DOI: https://doi.org/10.1090/proc/12825
Keywords: Commutator, pseudodifferential operator, paraproducts, bounded mean oscillation
Received by editor(s): July 8, 2014
Received by editor(s) in revised form: September 11, 2014
Published electronically: July 15, 2015
Additional Notes: This work was supported by NSF grant DMS-1161620
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2015 American Mathematical Society