English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The purpose of this paper is to study H\"older estimates for the$\bar\partial$ problem for $(p,q)$ forms on products of general planar domains.As indicated by an example of Stein and Kerzman, solutions to the$\bar\partial$ problem on product domains in $\mathbb C^n (n\ge 2)$ does notgain regularity in H\"older spaces. Making use of an integral representation ofNijenhuis and Woolf, we show that given a $\bar\partial$-closed $(p,q)$ formwith $C^{k,\alpha}$ components, $0\le p\le n, 1\le q\le n$, $k\in \mathbbZ^+\cup \{0\}, 0<\alpha\le 1$, there is a $C^{k, \alpha'}$ solution to the$\bar\partial$ problem on product domains for any $0<\alpha'<\alpha$ with thedesired H\"older estimate.

H\"older estimates for the $\bar\partial$ problem for $(p,q)$ forms on product domains