bounds for spectral multipliers on nilpotent groups
bounds for spectral multipliers on nilpotent groups
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DOI：
10.1090/s0002-9947-1991-1104196-7
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发表时间：
1991
影响因子：
1.3
通讯作者：
M. Christ
中科院分区：
文献类型：
--
作者：
M. Christ
本文给出了幂零李群上一类与左不变齐次椭圆二阶微分算子相关的谱乘子算子的LP有界性的一个判别准则，推广了Hormander关于欧氏空间上径向Fourier乘子的一个定理.所需的可微性的顺序是一半的齐次维数的组，改善了以前的结果在同一方向。
A criterion is given for the LP boundedness of a class of spec- tral multiplier operators associated to left-invariant, homogeneous subelliptic second-order differential operators on nilpotent Lie groups, generalizing a theo- rem of Hormander for radial Fourier multipliers on Euclidean space. The order of differentiability required is half the homogeneous dimension of the group, improving previous results in the same direction.