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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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Fourier multipliers in Banach function spaces with UMD concavifications
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by Alex Amenta, Emiel Lorist and Mark Veraar PDF
Trans. Amer. Math. Soc. 371 (2019), 4837-4868 Request permission

Abstract:

We prove various extensions of the Coifman–Rubio de Francia–Semmes multiplier theorem to operator-valued multipliers on Banach function spaces. Our results involve a new boundedness condition on sets of operators which we call ${\ell ^{r}(\ell ^{s})}$-boundedness, which implies $\mathcal {R}$-boundedness in many cases. The proofs are based on new Littlewood–Paley–Rubio de Francia-type estimates in Banach function spaces which were recently obtained by the authors.
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Additional Information
  • Alex Amenta
  • Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, 2600 GA Delft, The Netherlands
  • MR Author ID: 1089937
  • Email: Amenta@fastmail.fm
  • Emiel Lorist
  • Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, 2600 GA Delft, The Netherlands
  • MR Author ID: 1192948
  • ORCID: 0000-0002-2045-6035
  • Email: E.Lorist@tudelft.nl
  • Mark Veraar
  • Affiliation: Delft Institute of Applied Mathematics, Delft University of Technology, 2600 GA Delft, The Netherlands
  • MR Author ID: 775296
  • Email: M.C.Veraar@tudelft.nl
  • Received by editor(s): May 23, 2017
  • Received by editor(s) in revised form: December 5, 2017
  • Published electronically: September 20, 2018
  • Additional Notes: The authors were supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO)
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 4837-4868
  • MSC (2010): Primary 42B15; Secondary 42B25, 46E30, 47A56
  • DOI: https://doi.org/10.1090/tran/7520
  • MathSciNet review: 3934469