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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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Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces
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by Jarod Hart, Rodolfo H. Torres and Xinfeng Wu PDF
Trans. Amer. Math. Soc. 370 (2018), 8581-8612 Request permission

Abstract:

We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain several Leibniz-type rules in the context of Lebesgue and mixed Lebesgue spaces.
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Additional Information
  • Jarod Hart
  • Affiliation: Higuchi Biosciences Center, University of Kansas, Lawrence, Kansas 66047
  • MR Author ID: 863762
  • Email: jvhart@ku.edu
  • Rodolfo H. Torres
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7523
  • MR Author ID: 173635
  • ORCID: 0000-0002-3777-8671
  • Email: torres@ku.edu
  • Xinfeng Wu
  • Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7523
  • Address at time of publication: Department of Mathematics, China University of Mining & Technology, Beijing 100083, People’s Republic of China
  • Email: wuxf@ku.edu
  • Received by editor(s): January 20, 2017
  • Received by editor(s) in revised form: May 12, 2017
  • Published electronically: August 21, 2018
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 8581-8612
  • MSC (2010): Primary 42B20; Secondary 42B15, 47G99
  • DOI: https://doi.org/10.1090/tran/7312
  • MathSciNet review: 3864388