Weighted Koppelman-Leray-Norguet formulas on a local \(q\)-concave wedge in a complex manifold (Q1418270)

Various authors have proved generalizations of the Koppelman-Leray-Norguet homotopy formula for \(\overline\partial\) on differential forms. Some articles relevant to this paper are those of \textit{B. Berndtsson} and \textit{M. Andersson} [Ann. Inst. Fourier 32, No. 3, 91--110 (1982; Zbl 0466.32001)] on formulas with weight factors; of \textit{Ch. Laurent-Thiébaut} and \textit{J. Leiterer} [Astérisque 217, 151--182 (1993; Zbl 0796.32008)] on formulas for \(q\)-concave wedges in \({\mathbb C}^n\); and of \textit{T. Zhong} [J. Xiamen Univ., Nat. Sci. 38, No. 1, 5--10 (1999; Zbl 0939.32003)] on formulas for \(q\)-concave wedges in complex manifolds. In this paper the authors generalize the formula by obtaining Koppelman-Leray-Norguet formulas with weights on \(q\)-concave wedges in complex manifolds.