We prove regularity of solutions of the \(\bar{\partial }\)-problem in the Hölder–Zygmund spaces of bounded, strongly \(\mathbf{C}\)-linearly convex domains of class \(C^{1,1}\). The proofs rely on a new analytic characterization of said domains which is of independent interest, and on techniques that were recently developed by the first-named author to prove estimates for the \(\bar{\partial }\)-problem on strongly pseudoconvex domains of class \(C^2\).

中文翻译：

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$$ \ overline {\ partial} $$¯的正则性-强$$ \ mathbf {C} $$ C的求解算子-最小光滑度的线性凸域

我们证明了\（\ bar {\ partial} \）问题在有界，强烈\（\ mathbf {C} \） -类\（C ^ {1的线性凸域）的Hölder–Zygmund空间中的解的正则性，1} \）。证明依赖于具有独立利益的所述域的新分析特征，并且依赖于第一作者最近开发的技术，用于证明对强伪凸的\（\ bar {\ partial} \）问题的估计。类\（C ^ 2 \）的域。