A solution of an $L^{2}$ extension problem with optimal estimate and applications
A solution of an $L^{2}$ extension problem with optimal estimate and applications
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发表时间：
2013-10
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通讯作者：
Qi’an Guan;Xiangyu Zhou
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作者：
Qi’an Guan;Xiangyu Zhou
本文用精确的方法证明了一个具有最优估计的L^2扩张定理，它包含了各种著名的L^2扩张定理的最优估计形式.作为应用，我们在Suita猜想的等式条件下证明了Suita的一个猜想，即所谓的$L-$猜想和推广的Suita猜想.作为其它应用，我们肯定地回答了Ohsawa关于加权Bergman空间之间的扩张算子的极限情形的问题，并给出了我们的结果与Berglessson关于Bergman核的对数多重次调和性的重要结果的关系.
In this paper, we prove an $L^2$ extension theorem with optimal estimate in a precise way, which implies optimal estimate versions of various well-known $L^2$ extension theorems. As applications, we give proofs of a conjecture of Suita on the equality condition in Suita's conjecture, the so-called $L-$conjecture, and the extended Suita conjecture. As other applications, we give affirmative answer to a question by Ohsawa about limiting case for the extension operators between the weighted Bergman spaces, and we present a relation of our result to Berndtsson's important result on log-plurisubharmonicity of Bergman kernel.