Riesz transforms and multipliers for the Grushin operator

2011/10/14 by Jotsaroop, K., Sanjay, P. K., Thangavelu, S.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1110.3227

Abstract

We show that Riesz transforms associated to the Grushin operator G = -Δ- |x|²∂_t² are bounded on L^p(Rⁿ+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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