Dimension free boundedness of Riesz transforms for the Grushin operator

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 the dimension $n$.

12 pages. To appear in Proc. Amer. Math. Soc

References in corpus (2)

• Revisiting Riesz transforms on Heisenberg groups
• Riesz transforms and multipliers for the Grushin operator

Cited by in corpus (2)

• On Some Operators Associated with Non-Degenerate Symmetric $\alpha$-Stable Probability Measures
• Riesz transforms associated with the Grushin operator with drift