The Frolicher-type inequalities of foliations

The purpose of this article is to adapt the Frolicher-type inequality to the case of transversely holomorphic and transversely symplectic foliations. These inequalities can be used to e.g. determine whether a given foliation can be made transversely Kahler (due to their relations to various dd’-lemmas). Our main results can be also stated for orbifolds as we point out in section 5 of this paper.