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arXiv · 1210.3564

A sharp multiplier theorem for Grushin operators in arbitrary dimensions

Alessio Martini·Detlef Müller
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Abstract

In a recent work by A. Martini and A. Sikora (arXiv:1204.1159), sharp L^p spectral multiplier theorems for the Grushin operators acting on $R^{d_1} \times R^{d_2}$ are obtained in the case $d_1 \geq d_2$. Here we complete the picture by proving sharp results in the case $d_1 < d_2$. Our approach exploits L^2 weighted estimates with "extra weights" depending only on the second factor of $R^{d_1} \times R^{d_2}$ (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.

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Alessio Martini, Detlef Müller. 2012-10-12. A sharp multiplier theorem for Grushin operators in arbitrary dimensions. https://doi.org/10.4171/rmi%2F814

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