The �?-equation on a positive current

• DOI: 10.1007/s002220100178
• Publication Date: 2003-02-12T18:21:59Z
• Authors: Bo Berndtsson; Nessim Sibony
• Keywords: Harmonic

We study the induced ¯∂-equation on a positive current in a complex manifold. We extend the L 2-estimates for the ¯∂-equation to harmonic currents of bidimension (1,1), satisfying a Frobenius type condition. We also show that the L 2-estimates are satisfied for the ¯∂-equation on a positive closed current of bidegree (1,1) on a pseudoconvex domain in ℂ n .