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\(\mathcal C^{k+\alpha}\)-estimates for the \(\bar \partial\)-equation on the Hartogs triangle. (English) Zbl 0756.32002

On Hartogs triangle, \({\mathcal C}^{k+\alpha}\)-estimates for \(\overline\partial\) are shown for all non-negative \(k+\alpha\). This is done by pulling the problem back to the bidisc. A special solution, constructed there, can be pushed forward to the Hartogs triangle, in the course of which all estimates and regularity conditions are preserved.
Reviewer: L.Ma

MSC:

32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A40 Boundary behavior of holomorphic functions of several complex variables
32T99 Pseudoconvex domains
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References:

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