Riesz transforms and multipliers for the Grushin operator
Functional Analysis
2011-10-17 v1
Abstract
We show that Riesz transforms associated to the Grushin operator G = -\Delta - |x|^2\partial_t^2 are bounded on L^p(R^n+1). We also establish an analogue of H\"ormander-Mihlin multiplier theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator valued Fourier multiplier theorem due to L. Weis.
Cite
@article{arxiv.1110.3227,
title = {Riesz transforms and multipliers for the Grushin operator},
author = {K. Jotsaroop and P. K. Sanjay and S. Thangavelu},
journal= {arXiv preprint arXiv:1110.3227},
year = {2011}
}
Comments
14 pages