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Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition

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Abstract

We discuss local solvability of operators of the form\(\sum\limits_{j,k = 1}^{2n} {a_{jk} V_j V_k + i\alpha U} \) where theV j are left-invariant vector fields on the Heisenberg group such that [V j ,V j+n ]=U for 1≤j≤n andA=(a jk )=A 1+iA 2 is a complex symmetric matrix satisfying the “cone condition” |A 2|≤CA 1.

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Author notes

  1. Fulvio Ricci

    Present address: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy

Authors and Affiliations

  1. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, D-24098, Kiel, Germany

    Detlef Müller

  2. Dipartimento di Matematica, Politecnico di Torino, Torino, Italy

    Fulvio Ricci

Authors
  1. Detlef Müller
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  2. Fulvio Ricci
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Correspondence to Detlef Müller.

Additional information

The authors acknowledge the support for this work by the European Commission through the European HCM-program “Fourier Analysis” and the TMR network “Harmonic Analysis”.

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Müller, D., Ricci, F. Solvability of second-order left-invariant differential operators on the Heisenberg group satisfying a cone condition. J. Anal. Math. 89, 169–197 (2003). https://doi.org/10.1007/BF02893080

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  • DOI: https://doi.org/10.1007/BF02893080

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