Fourier integral operators on Hardy spaces with Hormander class

2024/06/05 by Ye, Xiaofeng, Zhang, Chunjie, Zhu, Xiangrong
#35S30 #42B20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.03076

Abstract

In this note, we consider a Fourier integral operator defined by Tϕ,af(x) = ∫ℝneiϕ(x,ξ)a(x,ξ)\widehatf ξ)dξ,here a is the amplitude, and ϕ is the phase. Let 0≤ρ≤ 1,n≥ 2 or 0≤ρ<1,n=1 and mp=(ρ-n)/(p)+(n-1)min\\frac 12,ρ\. If a belongs to the forbidden Hörmander class Smpρ,1 and ϕ∈ Φ2 satisfies the strong non-degeneracy condition, then for any \frac nn+1

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