 Cauchy-Green operator

ID: cauchy-green-operator

D \subset C

, the Cauchy-Green operator

T g (z) = \frac{1}{2 πi} \int_{D} \frac{g ( w )}{w - z} d w \land d \overset{w}{ˉ}

is a right inverse to

\partial / \partial \overset{z}{ˉ}

in the interior:

\partial_{\overset{z}{ˉ}} T g = g

. Applying it to coefficients gives the local homotopy operator used in the Dolbeault-Poincaré lemma.

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