Endpoint regularity of general Fourier integral operators

2024/08/19 by Zhu, Xiangrong, Li, Wenjuan
#35S30 #42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.15280

Abstract

Let n≥ 1,0<ρ<1, max\ρ,1-ρ\≤ δ≤ 1 and m1=ρ-n+(n-1)min\\frac 12,ρ\+\frac 1-δ2. If the amplitude a belongs to the Hörmander class Sm1ρ,δ and ϕ∈ Φ2 satisfies the strong non-degeneracy condition, then we prove that the following Fourier integral operator Tϕ,a defined by Tϕ,af(x)=∫ℝneiϕ(x,ξ)a(x,ξ)\widehatf(ξ)dξ, is bounded from the local Hardy space h1(ℝn) to L1(ℝn). As a corollary, we can also obtain the corresponding Lp(ℝn)-boundedness when 1

Related

• Fourier integral operators on Hardy spaces with Hormander class
• A class of multi-parameter Fourier integral operators: endpoint Hardy space bounds
• Notes on Regularity of Fourier integral operators with symbol in S^m_0,δ
• Regularity of Fourier integrals on product spaces
• L^p-boundedness of multi-parameter Fourier integral operators