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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 4, pp 599–612 | Cite as

Sobolev Spaces on Quasi-Kähler Complex Varieties

  • Haisheng LiuEmail author
Article

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) ↪ L2(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.

Keywords

Quasi-Kähler variety Sobolev spaces 

2000 MR Subject Classification

46E35 32W05 32Q99 

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Notes

Acknowledgement

The author wants to express great thanks to Prof. Kefeng Liu for many useful discussions and comments.

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Copyright information

© The Editorial Office of CAM and Springer-Verlag Berlin Heidelberg 2019

Authors and Affiliations

  1. 1.Center of Mathematical SciencesZhejiang UniversityHangzhouChina

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