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Transactions of the American Mathematical Society

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Smoothing properties of bilinear operators and Leibniz-type rules in Lebesgue and mixed Lebesgue spaces


Authors: Jarod Hart, Rodolfo H. Torres and Xinfeng Wu
Journal: Trans. Amer. Math. Soc. 370 (2018), 8581-8612
MSC (2010): Primary 42B20; Secondary 42B15, 47G99
DOI: https://doi.org/10.1090/tran/7312
Published electronically: August 21, 2018
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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
Email: jvhart@ku.edu

Rodolfo H. Torres
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-7523
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

DOI: https://doi.org/10.1090/tran/7312
Keywords: Bilinear operators, multipliers, maximal function, smoothing properties, fractional derivatives, Leibniz rule, mixed Lebesgue spaces
Received by editor(s): January 20, 2017
Received by editor(s) in revised form: May 12, 2017
Published electronically: August 21, 2018
Article copyright: © Copyright 2018 American Mathematical Society

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