Littlewood-Paley theorem for Schrödinger operators
Littlewood-Paley theorem for Schrödinger operators
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薛定谔算子的利特伍德-佩利定理
DOI：
10.1007/s10496-006-0353-1
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
Shijun Zheng
中科院分区：
文献类型：
--
作者：
Shijun Zheng
设H是ℝn上的薛定谔算子，在其谱算子核的多项式衰减条件下，证明了与H相伴的Besov空间和Triebel-Lizorkin空间是良好定义的.进一步利用H的并矢函数给出了Lp空间的Littlewood-Paley刻划，推广和加强了当H的热核满足一定的高斯界时的结果。
Let H be a Schrödinger operator on ℝn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.