The Dolbeault complex in infinite dimensions. II
Laszlo Lempert
Abstract
We prove that the equation d-bar u = f can be solved on a ball B(R) of radius R in the Banach space l1 if f is a closed Lipschitz continuous (0,1) form on B(R). We also present examples of closed (0,1) forms f of various regularities on the spaces lp that are not exact. In particular, in the first result above, it is not enough to assume that f is merely continuous, rather than Lipschitz continuous.
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