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About the Schauder Estimate in the paper of Yau regarding Calabi's conjecture

I'm trying to understand the paper Yau, S.-T., On The Ricci Curvature of a Compact Kähler Manifold and the Complex Monge-Ampére Equation, I, Comm. Pure Appl. Math., 31 (1978) 339-411 (DOI) Let $\...