On the $L^2\rightarrow L^\infty$ norms of spectral multipliers of “quasi-homogeneous” operators on homogeneous groups
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Abstract:
We study the $L^2 \to L^{\infty }$ norms of spectral projectors and spectral multipliers of left-invariant elliptic and subelliptic second-order differential operators on homogeneous Lie groups. We obtain a precise description of the $L^2 \to L^{\infty }$ norms of spectral multipliers for some class of operators which we call quasi-homogeneous. As an application we prove a stronger version of Alexopoulos’ spectral multiplier theorem for this class of operators.References
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Additional Information
- Adam Sikora
- Affiliation: Centre for Mathematics and Its Applications, School of Mathematical Sciences, Australian National University, Canberra ACT 0200, Australia
- MR Author ID: 292432
- Email: sikora@maths.anu.edu.au, sikora@math.uni.wroc.pl
- Received by editor(s): November 10, 1996
- Published electronically: April 27, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 3743-3755
- MSC (1991): Primary 42B15; Secondary 43A22, 35P99
- DOI: https://doi.org/10.1090/S0002-9947-99-02501-5
- MathSciNet review: 1670160