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We prove a regularity result for Green's functions that are associated toelliptic second order divergence-type linear PDO's with coefficients inC^{1,\alpha}(\bar{\Omega}). Here \alpha\in (0,1) and \Omega\subset \R^n is abounded C^{2,\alpha} domain in dimension n\ge 3. The regularity result givesboundary estimates for derivatives up to order (2+\alpha) and, by using theseestimates, we extend the associated Green's operator to a globally definedsingular integral which of Calder\'on--Zygmund type.

On extension of Green's operator on bounded smooth domains