Schrödinger equation on the Heisenberg group

Volume 161 / 2004

Jacek Zienkiewicz Studia Mathematica 161 (2004), 99-111 MSC: 35S10, 42B25. DOI: 10.4064/sm161-2-1

Abstract

Let $L$ be the full laplacian on the Heisenberg group ${{\mathbb H}}^n$ of arbitrary dimension $n$. Then for $f \in L^2({{\mathbb H}}^n)$ such that ${(I-L)}^{s / 2} f \in L^2({{\mathbb H}}^n)$ for some $s>{1 / 2}$ and for every $\phi \in C_{\rm c}({{\mathbb H}}^n)$ we have $$ \int _{{{\mathbb H}}^n} |\phi (x)| \mathop {\rm sup}_{0 < t \leq 1} |e^{\sqrt{-1}\, tL}f(x)|^2\, dx \leq C_{\phi }{\| f\| }^2_{W^s}. $$

Authors

  • Jacek ZienkiewiczInstitute of Mathematics
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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