TITLE: Dolbeault cohomology of Hopf manifolds
QUESTION [16 upvotes]: This should be straightforward; I'm sorry if it's too much so.  Can someone point me to a reference which computes the Dolbeault cohomology of the Hopf manifolds?
Motivation:  I'd like to work through a concrete example of the Hodge decomposition theorem failing for non-Kähler manifolds.  The textbook I have handy (Griffiths & Harris) doesn't treat this, and the obvious Google search was unhelpful.

REPLY [3 votes]: There are some references where it is computed
D. Mall, {\em The cohomology of line bundles on Hopf manifolds},
Osaka J. Math. {\bf 28} (1991), 999--1015.
D. Mall, {\em Contractions, Fredholm operators and the cohomology
of vector bundles on Hopf manifolds}, Arch. Math., {\bf 66} (1996), 71--76.
M. Ise, {\em On the geometry of Hopf manifolds}, Osaka J. Math.
{\bf 12} (1960), 387--402.
A. Libgober, {\em Cohomology of bundles on homological Hopf mani
folds},  Sci. China Ser. A {\bf 52} (2009), no. 12, 2688--2698.
A. Haefliger: Deformations of transversely holomorphic flows on spheres and deformations
of Hopf manifolds. Compositio Mathematica,55 (1985), 241-251.