Sobolev Spaces on Quasi-K\"ahler Complex Varieties

Citation:

Haisheng LIU.Sobolev Spaces on Quasi-K\"ahler Complex Varieties[J].Chinese Annals of Mathematics B,2019,40(4):599~612
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Authors:

Haisheng LIU;
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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