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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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