Hölder regularity of the $\bar\partial-$equation on the polydisc

Fuente: arXiv
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Autori principali: Loo, Yu Jun, Tumanov, Alexander
Natura: Preprint
Pubblicazione: 2023
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author Loo, Yu Jun
Tumanov, Alexander
author_facet Loo, Yu Jun
Tumanov, Alexander
contents In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves Hölder 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 Hölder regularity. Hence, this solution operator is optimal in that regard.
format Preprint
id arxiv_https___arxiv_org_abs_2301_04484
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Hölder regularity of the $\bar\partial-$equation on the polydisc
Loo, Yu Jun
Tumanov, Alexander
Complex Variables
Analysis of PDEs
In this note, we show the existence of a solution operator to the $\bar\partial-$equation in the polydisc that preserves Hölder 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 Hölder regularity. Hence, this solution operator is optimal in that regard.
title Hölder regularity of the $\bar\partial-$equation on the polydisc
topic Complex Variables
Analysis of PDEs
url https://arxiv.org/abs/2301.04484