Spectral multipliers on Lie groups of polynomial growth
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- by G. Alexopoulos
- Proc. Amer. Math. Soc. 120 (1994), 973-979
- DOI: https://doi.org/10.1090/S0002-9939-1994-1172944-4
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Abstract:
Let $L$ be a left invariant sub-Laplacian on a connected Lie group $G$ of polynomial volume growth, and let $\{ {E_\lambda },\lambda \geqslant 0\}$ be the spectral resolution of $L$ and $m$ a bounded Borel measurable function on $[0,\infty )$. In this article we give a sufficient condition on $m$ for the operator $m(L) = \smallint _0^\infty m(\lambda )d{E_\lambda }$ to extend to an operator bounded on ${L^p}(G),\;1 < p < \infty$, and also from ${L^1}(G)$ to weak-${L^1}(G)$.References
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Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 973-979
- MSC: Primary 22E30
- DOI: https://doi.org/10.1090/S0002-9939-1994-1172944-4
- MathSciNet review: 1172944