In a recent work by A. Martini and A. Sikora, sharp spectral multiplier theorems for the Grushin operators acting on and defined by the formula
are obtained in the case . Here we complete the picture by proving sharp results in the case . Our approach exploits weighted estimates with "extra weights" depending essentially on the second factor of (in contrast to the mentioned work, where the "extra weights" depend only on the first factor) and gives a new unified proof of the sharp results without restrictions on the dimensions.
Cite this article
Alessio Martini, Detlef Müller, A sharp multiplier theorem for Grushin operators in arbitrary dimensions. Rev. Mat. Iberoam. 30 (2014), no. 4, pp. 1265–1280DOI 10.4171/RMI/814