Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operators

Alessio Martini, Adam Sikora

Type: Article

Publication Date: 2012-01-01

Citations: 33

DOI: https://doi.org/10.4310/mrl.2012.v19.n5.a9

Abstract

We obtain weighted Plancherel estimates for the considered operators.As a consequence we prove L p spectral multiplier results and Bochner-Riesz summability for the Grushin operators.These results are sharp if d 1 ≥ d 2 .We discuss also an interesting phenomenon for weighted Plancherel estimates for d 1 < d 2 .The described spectral multiplier theorem is the analogue of the result for the sublaplacian on the Heisenberg group obtained by Müller and Stein and by Hebisch.

Locations

Mathematical Research Letters - View - PDF
arXiv (Cornell University) - View - PDF

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