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| Sobolev Spaces on Quasi-K\"ahler Complex Varieties |
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Citation： |
Haisheng LIU.Sobolev Spaces on Quasi-K\"ahler Complex Varieties[J].Chinese Annals of Mathematics B,2019,40(4):599~612 |
| Page view： 1736
Net amount： 1565 |
Authors： |
Haisheng LIU; |
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| Abstract： |
If $V$ is an irreducible quasi-K\"ahler complex variety and $E$ is a
vector bundle over $\mathrm{reg}(V)$, the author proves that
$W^{1,2}_{0}(\mathrm{reg}(V),E)=W^{1,2}(\mathrm{reg}(V),E)$, and
that for $\dim_{\mathbb{C}}\mathrm{reg}(V)>1$, the natural inclusion
$W^{1,2}(\mathrm{reg}(V),E)\hookrightarrow L^{2}(\mathrm{reg}(V),E)$
is compact, the natural inclusion
$W^{1,2}(\mathrm{reg}(V),E)\hookrightarrow
L^{\frac{2v}{v-1}}(\mathrm{reg}(V),E)$ is continuous. |
Keywords： |
Quasi-K"ahler variety, Sobolev spaces |
Classification： |
46E35, 32W05, 32Q99 |
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