5 citations · 23 across the 23 of their papers we have counts for
32 papers
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…
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…
The Fundamental Solution to on Quadric Manifolds -- Part 1. General Formulas
Albert Boggess, Andrew Raich
This paper is the first of a three part series in which we explore geometric and analytic properties of the Kohn Laplacian and its inverse on general quadric submanifolds of $\math…
Closed range estimates for on CR manifolds of hypersurface type
Joel Coacalle, Andrew Raich
The purpose of this paper is to establish sufficient conditions for closed range estimates on -forms, for some fixed , , for in both $…
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…
Boundary invariants and the closed range property for
Phillip S. Harrington, Andrew Raich
This paper provides a connection between two distinct branches of research in CR geometry -- namely, analytic and geometric conditions that suffice to establish the closed range of…