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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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