Abstract
Let \(\mathbb X\) be a noncompact symmetric space of rank one, and let \(\mathfrak h^1(\mathbb X)\) be a local atomic Hardy space. We prove the boundedness from \(\mathfrak {h}^1(\mathbb {X})\) to \(L^1(\mathbb {X})\) and on \(\mathfrak {h}^1(\mathbb {X})\) of some classes of Fourier integral operators related to the wave equation associated with the Laplacian on \(\mathbb X\), and we estimate the growth of their norms depending on time.
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Acknowledgements
The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). This work was partially supported by the Progetto PRIN 2015 “Varietà reali e complesse: geometria, topologia e analisi armonica”. The authors would like to thank Stefano Meda, Fulvio Ricci and Peter Sjögren for helpful discussions about this work.
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Bruno, T., Tabacco, A., Vallarino, M. (2019). Endpoint Results for Fourier Integral Operators on Noncompact Symmetric Spaces. In: Boggiatto, P., et al. Landscapes of Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05210-2_2
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DOI: https://doi.org/10.1007/978-3-030-05210-2_2
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