Sobolev Spaces on Quasi-Kähler Complex Varieties

Haisheng Liu

Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 599 -612.

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Chinese Annals of Mathematics, Series B ›› 2019, Vol. 40 ›› Issue (4) : 599 -612. DOI: 10.1007/s11401-019-0154-4
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Sobolev Spaces on Quasi-Kähler Complex Varieties

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Abstract

If V is an irreducible quasi-Kähler complex variety and E is a vector bundle over reg(V), the author proves that W 0 1,2(reg(V), E) = W1,2(reg(V), E), and that for dim reg(V) > 1, the natural inclusion W1,2(reg(V), E) ↪ L 2(reg(V), E) is compact, the natural inclusion ${W^{1,2}}\left( {{\rm{reg}}\left( V \right),\;E} \right)\hookrightarrow {L^{{{2v} \over {v - 1}}}}\left( {{\rm{reg}}\left( V \right),\;E} \right)$ is continuous.

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Quasi-Kähler variety / Sobolev spaces

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Haisheng Liu. Sobolev Spaces on Quasi-Kähler Complex Varieties. Chinese Annals of Mathematics, Series B, 2019, 40(4): 599-612 DOI:10.1007/s11401-019-0154-4

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