On sharper estimates of Ohsawa-Takegoshi $L^2$-extension theorem

Genki Hosono

On sharper estimates of Ohsawa-Takegoshi $L^2$-extension theorem

Complex Variables 2018-03-06 v2

Authors: Genki Hosono

Abstract

We present an $L^2$ -extension theorem with an estimate depending on the weight functions for domains in $\mathbb{C}$ . When the Hartogs domain defined by the weight function is strictly pseudoconvex, this estimate is strictly sharper than known optimal estimates. When the weight function is radial, we prove that our estimate provides the $L^2$ -minimum extension.

Keywords

L^2-extension theorem Ohsawa-Takegoshi weight function Hartogs domain strictly pseudoconvex L^2-minimum extension

Cite

@article{arxiv.1708.08269,
  title  = {On sharper estimates of Ohsawa-Takegoshi $L^2$-extension theorem},
  author = {Genki Hosono},
  journal= {arXiv preprint arXiv:1708.08269},
  year   = {2018}
}

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6 pages

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