Fourier Lebesgue空间和调制空间的非拟解析波前集
Wave-front sets in non-quasianalytic setting for Fourier Lebesgue and modulation spaces
摘要：
我们定义和研究波前集的加权傅立叶-勒贝格空间时的权重是温和的相关功能的一般序列$\{ M_p\} $满足小松的条件$(M.1) - (M.3)'$。特别是，当$\{ M_p\} $是Gevrey序列（$M_p = p!^s$，$s>1$），我们恢复了一些以前观察到的结果。此外，我们考虑了调制空间在相同条件下的波前集，并证明了与Fourier-Lebesgue型波前集相关的不变性。
英文摘要：
We define and study wave-front sets for weighted Fourier-Lebesgue spaces when the weights are moderate with respect to the associated functions for general sequences $\{ M_p\} $ which satisfy Komatsu's conditions $(M.1) - (M.3)'$. In particular, when $\{ M_p\} $ is the Gevrey sequence ($M_p = p!^s$, $s>1$) we recover some previously observed results. Furthermore, we consider wave-front sets for modulation spaces in the same setting, and prove the invariance property related to the Fourier-Lebesgue type wave-front sets.
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