3 citations · 7 across the 6 of their papers we have counts for
13 papers · 1 filter
The -problem on -domains
Debraj Chakrabarti, Phillip S. Harrington, Andrew Raich
Given a complex manifold containing a relatively compact domain, we give sufficient geometric conditions on the domain so that its -cohomology in degree (known…
Sobolev Regularity of the Bergman Projection on a Smoothly Bounded Stein Domain that is not Hyperconvex
Phillip S. Harrington
For every , we will construct a flat Kähler manifold and a relatively compact domain with smooth boundary that is Stein but not hyperconvex such t…
Maximal Estimates for the -Neumann Problem on Non-pseudoconvex domains
Phillip S. Harrington, Andrew Raich
It is well known that elliptic estimates fail for the -Neumann problem. Instead, the best that one can hope for is that derivatives in every direction but one can be…
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…