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

We reduce the problem of constructing a linear solution operator to the$\bar{\partial}$-equation on smoothly bounded weakly pseudoconvex domains,$\Omega$, in $\mathbb{C}^2$ to the problem of the boundary$\bar{\partial}_b$-equation. We show there is a solution operator to$\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\Omega)\cap{ker}\bar{\partial} \rightarrow W^{s}(\Omega)$ for all $s\ge 0$ if there is acorresponding solution operator to the $\bar{\partial}_b$-problem withanalogous regularity properties.

Exact regularity of the $\bar{\partial}$-problem with dependence on the $\bar{\partial}_b$-problem on weakly pseudoconvex domains in $\mathbb{C}^2$