Riesz transforms and multipliers for the Grushin operator
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We show that Riesz transforms associated to the Grushin operator G = −Δ − |x|2∼ t 2 are bounded on L p (ℝ n+1). We also establish an analogue of the 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.
KeywordsHeisenberg Group Singular Integral Operator Hermite Operator Fourier Multiplier Schwartz Function
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