Dimension free boundedness of Riesz transforms for the Grushin operator

Sanjay, P. K.; Thangavelu, S.

doi:10.1090/S0002-9939-2014-12143-5

Dimension free boundedness of Riesz transforms for the Grushin operator
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by P. K. Sanjay and S. Thangavelu

Proc. Amer. Math. Soc. 142 (2014), 3839-3851

DOI: https://doi.org/10.1090/S0002-9939-2014-12143-5

Published electronically: July 8, 2014

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Abstract:

Let $G = - \Delta _{\xi } - |\xi |^2 \frac {\partial ^2}{\partial \eta ^2}$ 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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