Subcritical approach to conformally invariant extension operators on the upper half space
Subcritical approach to conformally invariant extension operators on the upper half space
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DOI：
10.1016/j.jfa.2018.08.012
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发表时间：
2017-11
影响因子：
1.7
通讯作者：
Mathew R. Gluck
中科院分区：
文献类型：
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作者：
Mathew R. Gluck
在这项工作中，我们得到了尖锐的嵌入不等式的共形不变的积分扩张算子的家庭。这个家族包括经典的Poisson扩张算子和具有Riesz核的扩张算子。我们证明了这些不等式中的锐常数，并对相应的极值函数进行了分类。我们还计算了极值函数的扩张在边界处的极限行为。
In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes (among others) the classical Poisson extension operator and the extension operator with Riesz kernel. We show that the sharp constants in these inequalities are attained and classify the corresponding extremal functions. We also compute the limiting behavior at the boundary of the extensions of the extremal functions.