Holomorphic L^{p}-functions on Coverings of Strongly Pseudoc(2)

In this paper we will show how to construct holomorphic L^{p}-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.

LetM NbeadomainwithsmoothboundarybMinann-dimensionalcomplexmanifoldN,speci cally,

M={z∈N:ρ(z)<0}(1.1)

whereρisareal-valuedfunctionofclassC2( )inaneighbourhood ofthecompactset

zj(z)wj=0}.(1.3)

TheLeviformofρatz∈bMisahermitianformonTzc(bM)de nedinthelocalcoordinatesbytheformula

Lz(w, zj wk.(1.4)

ThemanifoldMiscalledstronglypseudoconvexifLz(w,