Endpoint results for Fourier integral operators on noncompact symmetric spaces

TL;DR

This paper establishes boundedness properties of certain Fourier integral operators related to the wave equation on noncompact rank-one symmetric spaces, providing estimates on their norms' growth over time.

Contribution

It proves boundedness of specific Fourier integral operators from local Hardy space to L^1 and within Hardy space on noncompact symmetric spaces, with time-dependent norm estimates.

Findings

Boundedness from h^1(X) to L^1(X)

Boundedness on h^1(X)

Norm growth estimates depending on time

Abstract

Let X be a noncompact symmetric space of rank one and let h^1(X) be a local atomic Hardy space. We prove the boundedness from h^1(X) to L^1(X) and on h^1(X) of some classes of Fourier integral operators related to the wave equation associated with the Laplacian on X and we estimate the growth of their norms depending on time.