Constructing a homotopy formula demonstrates gains in derivative for a_q domains in complex manifolds, implying improvements in analysis methods.
We construct a global homotopy formula for aq a q domains in a complex manifold. The homotopy operators in the formula will gain 1/2 derivative in Hölder-Zygmund spaces Λ ʳ Λ r when the boundaries of the domains are in Λ ʳ⁺³ Λ r + 3 with $$r>0$$ r > 0 .
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Gong et al. (2025) studied this question.
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