Vanishing theorems for (k, s)-positive vector bundles on weakly pseudoconvex Kahler manifolds

We will use analytic methods in this paper, based on L-2-methods for the (partial derivative) over bar -equation, to obtain some new vanishing theorems for holomorphic vector bundles of (k, s)-positivity on weakly pseudoconvex Kahler manifolds which generalize those obtained by Demailly for s-positive vector bundles in his sense.