Endpoint results for Fourier integral operators on noncompact symmetric spaces

2016/09/23 by Tommaso Bruno, Bruno, Tommaso, Anita Tabacco +3 · 1 citation
Mathematics · #30H10 #35S30 #42B20 #53C35 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:30H10 #msc:35S30 #msc:42B20 #msc:53C35

paper · pdf · doi:10.48550/arxiv.1609.07401

22 pages

arxiv created 2018/04/09 · arxiv updated 2018/04/10

Abstract

Let X be a noncompact symmetric space of rank one and let h¹(X) be a local atomic Hardy space. We prove the boundedness from h¹(X) to L¹(X) and on h¹(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.

Cited by

• Sharp L^p-estimates for wave equation on ax+b groups

Related

• A multi-parameter family of Fourier integral operators
• Regularity of Fourier integrals on product spaces
• Global boundedness of multilinear Fourier integral operators
• A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds
• Weighted Fourier inequalities and application of restriction theorems on rank one Riemannian symmetric spaces of noncompact type