Abstract
We show that Riesz transforms associated to the Grushin operator G = −Δ − |x|2∼ 2 t are bounded on L p(ℝn+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.
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The second author is supported by the All India Council for Technical Education (AICTE).
The last author is supported by J. C. Bose Fellowship from the Department of Science and Technology (DST).
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Jotsaroop, K., Sanjay, P.K. & Thangavelu, S. Riesz transforms and multipliers for the Grushin operator. JAMA 119, 255–273 (2013). https://doi.org/10.1007/s11854-013-0008-z
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DOI: https://doi.org/10.1007/s11854-013-0008-z