Uniform estimates for \(\bar \partial\) on the intersection of two strictly pseudoconvex \(\mathbb C^2\)-domains without transversality condition
Integral operators are constructed for solving the inhomogeneous Cauchy-Riemann equation on arbitrary intersections of two smooth, strictly pseudoconvex domains and uniform estimates for these operators are proved. This means that we generalize a result of \textit{P. L. Polyakov} [Mat. Sb., N. Ser. 88(130), 238--255 (1972; Zbl 0276.32009)] and \textit{R. M. Range} and \textit{Y.-T. Siu} [Math. Ann. 206, 325--354 (1973; Zbl 0248.32015)] from 1972/73. They constructed integral operators for solving the Cauchy-Riemann equation with uniform estimates on finite intersections of smooth, strictly pseudoconvex domains. But they used the additional hypothesis that these domains intersect transversally. In the paper we answer the question, whether the hypothesis on transversality can be omitted, affirmatively.
scientific article; zbMATH DE number 4065410