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arXiv · 2301.04484

H\"older regularity of the $\bar\partial-$equation on the polydisc

Yu Jun Loo·Alexander Tumanov
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Abstract

In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves H\"older regularity. This solution operator is constructed using Henkin's formula. It is a well-known fact that solution operators to the $\bar\partial-$equation on product domains do not improve H\"older regularity. Hence, this solution operator is optimal in that regard.

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Yu Jun Loo, Alexander Tumanov. 2023-01-11. H\"older regularity of the $\bar\partial-$equation on the polydisc. https://doi.org/10.1080/17476933.2025.2598773

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