Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 959–966 | Cite as

Green-type identities for Rockland operators on graded Lie groups

  • Manat MustafaEmail author
  • Durvudkhan Suragan


This paper considers the analogues of Green-type formulae for Rockland operators on graded Lie groups. Furthermore, we also discuss some of their consequences.


Rockland operator Graded Lie group Green-type identity Representation formula 

Mathematics Subject Classification

35R03 35S15 


  1. 1.
    Cardona, D., Ruzhansky, M.: Multipliers for Besov spaces on graded Lie groups. C. R. Acad. Sci. Paris 355, 400–405 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Fischer, V., Ruzhansky, M.: Lower bounds for operators on graded Lie groups, C. R. Acad. Sci. Paris. Ser I. 351, 13–18 (2013)Google Scholar
  3. 3.
    Fischer, V., Ruzhansky, M.: Sobolev spaces on graded groups. Ann. Inst. Fourier (Grenoble) 67, 1671–1723 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Fischer, V., Ruzhansky, M.: A pseudo-differential calculus on graded nilpotent Lie groups. In Fourier Analysis, Trends in Mathematics, pp. 107–132, Birkhauser (2014)Google Scholar
  5. 5.
    Fischer, V., Ruzhansky, M.: Quantization on Nilpotent Lie Groups. Progress in Mathematics. Birkhäuser, Cham (2016)CrossRefzbMATHGoogle Scholar
  6. 6.
    Folland, G.B.: Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Mat. 13, 161–207 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Helffer, B., Nourrigat, J.: Caracterisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe de Lie nilpotent gradué. Comm. Partial Differ. Eq. 4(8), 899–958 (1979)CrossRefzbMATHGoogle Scholar
  8. 8.
    Gaveau, B.: Principle de moindre action, propagation de la chaleur et estimees sous elliptiques sur certains groupes nilpotents. Acta Math. 139, 95–153 (1977)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Geller, D.: Liouville’s theorem for homogeneous groups. Comm. Partial Differ. Eq. 8, 1665–1677 (1983)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Rockland, C.: Hypoellipticity on the Heisenberg group-representation-theoretic criteria. Trans. Am. Math. Soc. 240, 1–52 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ruzhansky, M., Suragan, D.: On Kac’s principle of not feeling the boundary for the Kohn Laplacian on the Heisenberg group. Proc. Am. Math. Soc. 144(2), 709–721 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Ruzhansky, M., Suragan, D.: Layer potentials, Kac’s problem, and refined Hardy inequality on homogeneous Carnot groups. Adv. Math 308, 483–528 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Ruzhansky, M., Suragan, D.: A comparison principle for nonlinear heat Rockland operators on graded groups. Bull. London Math. Soc. (2018).

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, School of Science and TechnologyNazarbayev UniversityAstanaKazakhstan

Personalised recommendations