ESTIMATES FOR UNIMODULAR FOURIER MULTIPLIERS ON MODULATION SPACES
ESTIMATES FOR UNIMODULAR FOURIER MULTIPLIERS ON MODULATION SPACES
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DOI：
10.1090/s0002-9939-09-09968-7
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发表时间：
2009-11
期刊：
影响因子：
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通讯作者：
Akihiko Miyachi;F. Nicola;S. Rivetti;A. Tabacco;Naohito Tomita
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文献类型：
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作者：
Akihiko Miyachi;F. Nicola;S. Rivetti;A. Tabacco;Naohito Tomita
研究了具有无界二阶导数的实值函数μ(ξ的符号为e^iμ的傅里叶乘子在调制空间上的作用。在一个简化的形式中，我们的结果如下：如果μ满足α≥2阶的通常的符号估计，或者如果μ是α次的正齐次函数，则对应的傅立叶乘子作为加权调制空间M^{p，q}_S和M^{p，q}之间的算子有界，对于所有的1≤p，q≤∞和S≥(α−2)n|1/p−1/2|。在这里，S代表了衍生品的损失。以上阈值对于任何齐次函数μ来说都是尖锐的，其海森矩阵在某个点上是非退化的
We study the action on modulation spaces of Fourier multipliers with symbols e^iμ(ξ), for real-valued functions μ having unbounded second derivatives. In a simplified form our result reads as follows: if μ satisfies the usual symbol estimates of order α ≥ 2, or if μ is a positively homogeneous function of degree α, then the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces M^{p,q}_s and M^{p,q}, for all 1 ≤ p, q ≤ ∞ and s ≥ (α − 2)n|1/p − 1/2|. Here s represents the loss of derivatives. The above threshold is shown to be sharp for any homogeneous function μ whose Hessian matrix is non-degenerate at some point