Notes on Regularity of Fourier integral operators with symbol in S^m_0,δ

2024/11/30 by Guangqing Wang, Wang, Guangqing, Suixin He +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2412.00409

Abstract

Let T_a,φ be a Fourier integral operator defined with a∈ S^m_0,δ(0≤δ<1) and φ∈ Φ² satisfying the strong non-degenerate condition. We demonstrate that when the order satisfies m≤-(n)/(2)-(n)/(p)δ+(n)/(p), the operator T_a,φ becomes bounded on L^p(ℝⁿ) for 2< p<∞ and maps L^∞(ℝⁿ) to BMO(ℝⁿ) when p=∞. Furthermore, the derived bound on m is sharp for L^p estimates in the case δ=0, and for (L^∞,BMO) when 0≤δ<1.

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