Abstract
In this paper, we prove an L 2 extension theorem with an 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 armative 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 the Bergman kernel.
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