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Let X be a compact K\"ahler manifold. In this paper we study the existence of constant weighted scalar curvature K\"ahler (weighted cscK) metrics on X. More precisely, we establish a priori C^k-estimates (k 0) for the K\"ahler potential associated with these metrics, thereby extending a result due to Chen and Cheng in the classical cscK setting.
Nezza et al. (Sat,) studied this question.
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