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.

Similarlyforp=1wehavefrom(2.1)withha:=hs,z

sup

w∈M|(Tψ,z(a))(y)|ψ(y):=sup y∈r 1(w) w∈M y∈r 1(w)s∈S

s∈S |as|ψ(z,s)· supsupw∈M s∈S |Fs,z(y)| asFs,z(y) ψ(y) ≤

y∈r 1(w)