Sobolev spaces on quasi-Kähler complex varieties. (English) Zbl 1429.46025
Summary: If \(V\) is an irreducible quasi-Kähler complex variety and \(E\) is a vector bundle over \(\mathrm{reg}(V)\), the author proves that \(W_0^{1,2}(\mathrm{reg}(V),E)=W^{1,2}(\mathrm{reg}(V),E)\), 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.
MSC:
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 58D15 | Manifolds of mappings |
| 32W05 | \(\overline\partial\) and \(\overline\partial\)-Neumann operators |
| 32Q99 | Complex manifolds |
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