A $T(1)$-theorem in relation to a semigroup of operators and applications to new paraproducts
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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.References
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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