7 citations · 16 across the 8 of their papers we have counts for
8 papers
On the Poincaré inequality on open sets in
A. -K. Gallagher
We show that the Poincaré inequality holds on an open set if and only if admits a smooth, bounded function whose Laplacian has a positive lower bound on…
On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces
Anne-Katrin Gallagher, Purvi Gupta, Liz Vivas
Given a holomorphic vector bundle over a compact Riemann surface , and an open set in , we prove that the Bergman space of holomorphic sections of the restriction of…
On plurisubharmonic defining functions for pseudoconvex domains in
Anne-Katrin Gallagher, Tobias Harz
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in . In particular, we construct a family o…
On the dimension of Bergman spaces on
Anne-Katrin Gallagher, Purvi Gupta, Liz Vivas
Inspired by a result by Szőke, we give potential-theoretic characterizations of the dimension of the Bergman space of holomorphic sections of a restriction of a holomorphic line bu…
Hardy Spaces for a Class of Singular Domains
Anne-Katrin Gallagher, Purvi Gupta, Loredana Lanzani +1
We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filt…
The closed range property for the -operator on planar domains
A. -K. Gallagher, J. Lebl, K. Ramachandran
Let be an open set. We show that has closed range in if and only if the Poincaré-Dirichlet inequality holds. Moreover, we give…
Convexity of level lines of Martin functions and applications
A. -K. Gallagher, J. Lebl, K. Ramachandran
Let be an unbounded domain in A positive harmonic function on that vanishes on the boundary of is called a Martin function. In thi…
On the dimension of the Bergman space for some unbounded domains
A. -K. Gallagher, T. Harz, G. Herbort
A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one…