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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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A $T(1)$-theorem in relation to a semigroup of operators and applications to new paraproducts
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by Frédéric Bernicot PDF
Trans. Amer. Math. Soc. 364 (2012), 6071-6108 Request permission

Abstract:

In this work, we are interested in developing new directions of the famous $T(1)$-theorem. More precisely, we develop a general framework where we look to replace the John-Nirenberg space $BMO$ (in the classical result) by a new $BMO_{L}$, associated to a semigroup of operators $(e^{-tL})_{t>0}$. These new spaces $BMO_L$ (including $BMO$) have recently appeared in numerous works in order to extend the theory of Hardy and $BMO$ space to more general situations. Then we give applications by describing boundedness for a new kind of paraproduct, built on the considered semigroup. In addition we obtain a version of the classical $T(1)$-theorem for doubling Riemannian manifolds.
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Additional Information
  • Frédéric Bernicot
  • Affiliation: CNRS - Laboratoire Paul Painlevé, Université Lille 1, 59655 Villeneuve d’Ascq Cedex, France
  • Address at time of publication: CNRS - Laboratoire Jean Leray, Université de Nantes, 2, rue de la Houssinière, 44322 Nantes, cedex 3, France
  • Email: frederic.bernicot@math.univ-lille1.fr
  • Received by editor(s): April 22, 2010
  • Received by editor(s) in revised form: April 25, 2011
  • Published electronically: April 30, 2012
  • © 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), 6071-6108
  • MSC (2010): Primary 30E20, 42B20, 42B30
  • DOI: https://doi.org/10.1090/S0002-9947-2012-05609-1
  • MathSciNet review: 2946943