多参数和多线性傅立叶乘法算子的尖锐霍曼德估计值

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-06-01 DOI:10.1007/s00208-024-02893-x

Jiao Chen, Danqing He, Guozhen Lu, Bae Jun Park, Lu Zhang

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引用次数: 0

摘要

在本文中，我们研究了多线性和多参数傅里叶乘数的霍曼德类型定理。当乘数是由\(1<u\le 2\) 的基于 \(L^u\)-based Sobolev norms 来描述时，在多参数和双线性情况下，我们关于平稳性假设的结果是尖锐的。在多参数和多线性情况下，我们的结果几乎是尖锐的。此外，即使在单参数和多线性情况下，我们的结果也改进了早期文献中的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A sharp Hörmander estimate for multi-parameter and multi-linear Fourier multiplier operators

In this paper, we investigate the Hörmander type theorems for the multi-linear and multi-parameter Fourier multipliers. When the multipliers are characterized by \(L^u\)-based Sobolev norms for \(1<u\le 2\), our results on the smoothness assumptions are sharp in the multi-parameter and bilinear case. In the multi-parameter and multi-linear case, our results are almost sharp. Moreover, even in the one-parameter and multi-linear case, our results improve earlier ones in the literature.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.