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The Endpoint Estimate for Fourier Integral Operators

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Abstract

Let Ta,ϕ be a Fourier integral operator defined by the oscillatory integral

$${T_{a,\varphi }}u(x) = {1 \over {{{(2\pi )}^n}}}\int_{{^n}} {{e^{{\rm{i}}\varphi (x,\xi )}}} a(x,\xi )\hat u(\xi ){\rm{d}}\xi,$$

where\(a \in S_{\varrho,\delta }^m\) and ϕ ∈ Φ2, satisfying the strong non-degenerate condition. It is shown that if 0 < ϱ ≤ 1, 0 ≤ δ < 1 and \( \le {{{\varrho ^2} - n} \over 2}\), then Ta,ϕ is a bounded operator from L∞(ℝn) to BMO(ℝn).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Guangqing Wang & Wenyi Chen

  2. College of Mathematics and System Science, Xinjiang University, Xinjiang, Ürümqi, 830046, China

    Jie Yang

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  1. Guangqing Wang
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  2. Jie Yang
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  3. Wenyi Chen
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Correspondence to Jie Yang.

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Wang, G., Yang, J. & Chen, W. The Endpoint Estimate for Fourier Integral Operators. Acta Math Sci 41, 426–436 (2021). https://doi.org/10.1007/s10473-021-0207-0

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  • DOI: https://doi.org/10.1007/s10473-021-0207-0

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