Exact regularity of $\bar{\partial}$ on pseudoconvex domains in $\mathbb{C}^2$

Dariush Ehsani

arxiv: 1508.04915 · v2 · pith:V55JPUDFnew · submitted 2015-08-20 · 🧮 math.CV

Exact regularity of bar{partial} on pseudoconvex domains in mathbb{C}²

Dariush Ehsani This is my paper

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keywords partialomegaboundeddomainsexactmathbbmboxoperator

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We show there is a solution operator to $\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\Omega)\cap\mbox{ker }\bar{\partial}\rightarrow W^{s}(\Omega)$ for all $s\ge 0$.

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Exact regularity of bar{partial} on pseudoconvex domains in mathbb{C}²

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