On $\overline{\partial }$ homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates

Liding Yao, Yuan Zhang

We construct homotopy formulae $f=\overline{\partial }{\mathcal{H}}_{q}f+{\mathcal{H}}_{q+1}\overline{\partial }f$ for $(0,q)$ forms on the product domain ${\Omega }_1\times \cdots \times {\Omega }_m$, where each…