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Journal d'Analyse Mathématique

, Volume 119, Issue 1, pp 255–273 | Cite as

Riesz transforms and multipliers for the Grushin operator

  • K. JotsaroopEmail author
  • P. K. Sanjay
  • S. Thangavelu
Article

Abstract

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.

Keywords

Heisenberg Group Singular Integral Operator Hermite Operator Fourier Multiplier Schwartz Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2013

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of MathematicsNational Institute of TechnologyCalicutIndia

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