乘积空间上傅里叶积分的正则性

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-08-19 DOI:arxiv-2408.09691

Chaoqiang Tan, Zipeng Wang

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引用次数: 0

摘要

我们通过让傅里叶积分算子的符号满足 R^N 上的多参数微分不等式来研究傅里叶积分算子族。我们证明，这些阶数为-(N-1)/2 的算子从经典、原子可分解的 H^1-Hardy 空间到 L^1(R^N) 都是有界的。因此，我们得到了 Seeger、Sogge 和 Stein 提出的一个尖锐的 L^p-regularity 结果。

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Regularity of Fourier integrals on product spaces

We study a family of Fourier integral operators by allowing their symbols to satisfy a multi-parameter differential inequality on R^N. We show that these operators of order -(N-1)/2 are bounded from classical, atom decomposable H^1-Hardy space to L^1(R^N). Consequently, we obtain a sharp L^p-regularity result due to Seeger, Sogge and Stein.

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arXiv - MATH - Classical Analysis and ODEs

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