A sharp multiplier theorem for Grushin operators in arbitrary dimensions

الأصل · EN

In a recent work by A. Martini and A. Sikora (arXiv:1204.1159), sharp Lᵖ spectral multiplier theorems for the Grushin operators acting on Rᵈ¹ × Rᵈ² are obtained in the case d₁ ≥ d₂. Here we complete the picture by proving sharp results in the case d₁ < d₂. Our approach exploits L² weighted estimates with "extra weights" depending only on the second factor of Rᵈ¹ × Rᵈ² (in contrast with the mentioned work, where the "extra weights" depend on the first factor) and gives a new unified proof of the sharp results without restrictions on the dimensions.