3 citations · 7 across the 6 of their papers we have counts for
10 papers
Exact sequences and estimates for the -problem
Debraj Chakrabarti, Phil Harrington
We study Sobolev estimates for solutions of the inhomogenous Cauchy-Riemann equations on annuli in $\cx^n$, by constructing exact sequences relating the Dolbeault cohomology of the…
On Competing Definitions for the Diederich-Fornæss Index
Phillip S. Harrington
Let be a bounded pseudoconvex domain. We define the Diederich-Fornæss index with respect to a family of functions to be the supremum over the set of all expo…
The -Neumann operator with the Sobolev norm of integer orders
Phillip Harrington, Bingyuan Liu
Let be a bounded pseudoconvex domain with smooth boundary. For each , we give a sufficient condition to estimate the -Neumann o…
Strong Closed Range Estimates: Necessary Conditions and Applications
Phillip S. Harrington, Andrew Raich
The theory of the operator on domains in is predicated on establishing a good basic estimate. Typically, one proves not a single basic estimate…
A Modified Morrey-Kohn-Hörmander Identity and Applications
Debraj Chakrabarti, Phillip S. Harrington
We prove a modified form of the classical Morrey-Kohn-Hörmander identity, adapted to pseudoconcave boundaries. Applying this result to an annulus between two bounded pseudoconvex d…
Hartogs Domains and the Diederich Fornæss Index
Muhenned Abdulsahib, Phillip S. Harrington
We study a geometric property of the boundary on Hartogs domains which can be used to find upper and lower bounds for the Diederich-Fornæss Index. Using this, we are able to show t…