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Let D be a strictly convex domain and X be a singular analytic subset of C^2such that the intersection of X and D is non empty. We give conditions underwhich a function holomophic on the intersection of X and D can be extendedholomorphically to D with growth estimates of BMO or L^q type. The extension isgiven by mean of integral representation formulas and new residual currents.

Extension with growth estimates of holomorphic functions defined on singular analytic spaces