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 Page view： 1017        Net amount： 897 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 Download PDF Full-Text