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Dimension free boundedness of Riesz transforms for the Grushin operator


Authors: P. K. Sanjay and S. Thangavelu
Journal: Proc. Amer. Math. Soc. 142 (2014), 3839-3851
MSC (2010): Primary 42Cxx, 42C05, 43A65
DOI: https://doi.org/10.1090/S0002-9939-2014-12143-5
Published electronically: July 8, 2014
MathSciNet review: 3251724
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Abstract: Let $ G = - \Delta _{\xi } - \vert\xi \vert^2 \frac {\partial ^2}{\partial \eta ^2}$ be the Grushin operator on $ \mathbb{R}^n \times \mathbb{R}.$ We prove that the Riesz transforms associated to this operator are bounded on $ L^p (\mathbb{R}^{n+1}), 1 < p < \infty $, and their norms are independent of dimension $ n$.


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Additional Information

P. K. Sanjay
Affiliation: Department of Mathematics, National Institute of Technology, Calicut 673 601, India
Address at time of publication: Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
Email: sanjay@math.iisc.ernet.in

S. Thangavelu
Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
Email: veluma@math.iisc.ernet.in

DOI: https://doi.org/10.1090/S0002-9939-2014-12143-5
Received by editor(s): August 11, 2012
Received by editor(s) in revised form: November 17, 2012
Published electronically: July 8, 2014
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2014 American Mathematical Society