Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
Strong hypercontractivity and logarithmic Sobolev inequalities on stratified complex Lie groups
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DOI：
10.1090/tran/7200
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发表时间：
2015-10
期刊：
影响因子：
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通讯作者：
Nathaniel Eldredge;L. Gross;L. Saloff‐Coste
中科院分区：
文献类型：
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作者：
Nathaniel Eldredge;L. Gross;L. Saloff‐Coste
我们证明了对于复李群上的次椭圆狄利克雷形式算子a，如果对数Sobolev不等式成立，则a的全纯投影在Janson意义上是强超收缩的。这将Gross先前的结果推广到算子a不是全纯的情况。
We show that for a hypoelliptic Dirichlet form operator A on a stratified complex Lie group, if the logarithmic Sobolev inequality holds, then a holomorphic projection of A is strongly hypercontractive in the sense of Janson. This extends previous results of Gross to a setting in which the operator A is not holomorphic.