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Rockland operators and Sobolev spaces

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Part of the Progress in Mathematics book series (PM,volume 314)


In this chapter, we study a special type of operators: the (homogeneous) Rockland operators. These operators can be viewed as a generalisation of sub-Laplacians to the non-stratified but still homogeneous (graded) setting. The terminology comes from a property conjectured by Rockland and eventually proved by Helffer and Nourrigat in [HN79], see Section 4.1.3.


  • Sobolev Space
  • Heat Kernel
  • Functional Calculus
  • Fractional Power
  • Convolution Kernel

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Fischer, V., Ruzhansky, M. (2016). Rockland operators and Sobolev spaces. In: Quantization on Nilpotent Lie Groups. Progress in Mathematics, vol 314. Birkhäuser, Cham.

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