Sobolev Spaces on Quasi-Kähler Complex Varieties

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) = W^1,2(reg(V), E), and that for dim_ℂ reg(V) > 1, the natural inclusion W^1,2(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.

Keywords

Quasi-Kähler variety / Sobolev spaces