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Endpoint Results for Fourier Integral Operators on Noncompact Symmetric Spaces

  • Tommaso Bruno
  • Anita Tabacco
  • Maria VallarinoEmail author
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

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.

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche “Giuseppe Luigi Lagrange”Politecnico di TorinoTorinoItaly

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