Abstract
We consider a class of spectral multipliers on stratified Lie groups which generalise the class of Hörmander multipliers and include multipliers with an oscillatory factor. Oscillating multipliers have been examined extensively in the Euclidean setting where sharp, endpoint L p estimates are well known. In the Lie group setting, corresponding L p bounds for oscillating spectral multipliers have been established by several authors but only in the open range of exponents. In this paper we establish the endpoint L p(G) bound when G is a stratified Lie group. More importantly we begin to address whether these estimates are sharp.
In honour of Fulvio Ricci on his 70th birthday
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Acknowledgements
We would like to thank Alessio Martini and Steve Wainger for discussing the history of the problem as well as guiding us through the literature. We also wish to thank the referee for many helpful comments and suggestions.
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Ciatti, P., Wright, J. (2021). Strongly Singular Integrals on Stratified Groups. In: Ciatti, P., Martini, A. (eds) Geometric Aspects of Harmonic Analysis. Springer INdAM Series, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-030-72058-2_8
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