Regularity of Morrey commutators
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- by David R. Adams and Jie Xiao PDF
- Trans. Amer. Math. Soc. 364 (2012), 4801-4818 Request permission
Abstract:
This paper is devoted to presenting a new proof of boundedness of the commutator $bI_\alpha -I_\alpha b$ (in which $I_\alpha$ and $b$ are regarded as the Riesz and multiplication operators) acting on the Morrey space $L^{p,\lambda }$ under $b\in \operatorname {BMO}$, and naturally, developing a regularity theory of commutators for Morrey-Sobolev spaces $I_\alpha (L^{p,\lambda })$ via a completely original iteration of $I_\alpha$. Even in the special case of $I_\alpha (L^p)$, this is a new theory.References
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Additional Information
- David R. Adams
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
- Email: dave@ms.uky.edu
- Jie Xiao
- Affiliation: Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland & Labrador, Canada A1C 5S7
- MR Author ID: 247959
- Email: jxiao@mun.ca
- Received by editor(s): November 4, 2010
- Published electronically: April 6, 2012
- Additional Notes: The second author was supported in part by NSERC of Canada.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 4801-4818
- MSC (2010): Primary 42B35, 46E35, 47G10
- DOI: https://doi.org/10.1090/S0002-9947-2012-05595-4
- MathSciNet review: 2922610