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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Regularity of Morrey commutators


Authors: David R. Adams and Jie Xiao
Journal: Trans. Amer. Math. Soc. 364 (2012), 4801-4818
MSC (2010): Primary 42B35, 46E35, 47G10
Published electronically: April 6, 2012
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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.


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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
Email: jxiao@mun.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05595-4
PII: S 0002-9947(2012)05595-4
Keywords: Morrey-Sobolev spaces, commutators, traces, weights, Choquet integrals, fractional Laplacians, Riesz integrals, maximal operators
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.