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arXiv · 1110.3227

Riesz transforms and multipliers for the Grushin operator

K. Jotsaroop·P. K. Sanjay·S. Thangavelu
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Abstract

We show that Riesz transforms associated to the Grushin operator G = -Δ- |x|^2\partial_t^2 are bounded on L^p(R^n+1). We also establish an analogue of Hörmander-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.

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K. Jotsaroop, P. K. Sanjay, S. Thangavelu. 2011-10-14. Riesz transforms and multipliers for the Grushin operator. https://arxiv.org/abs/1110.3227

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