Luke Edholm
Personal Information
Email：luke.david.edholm@univie.ac.at
Office：06.136
Phone：+43 1 4277 9803269
Address：Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Orcid iD: 0000-0001-8659-8864
Research Interests
I work in analysis, mainly in several complex variables, CR geometry, harmonic analysis and special function theory. I use integral operators like the Bergman projection, Szegö projection, the Leray transform and other Cauchy-Fantappiè integrals to relate holomorphic function theory to geometry. I am interested in the mapping properties of these operators (particularly in the presence of boundary singularities), along with the development of new operators with more refined properties.
CV (updated September 2024)
DOWNLOAD
File size: 196 kB
Preprints (submitted)
DOWNLOAD
File size: 646 kB
Preprints (accepted)
Publications
Edholm LD, Shelah Y. The Leray transform: distinguished measures, symmetries and polygamma inequalities. Journal of Functional Analysis. 2025 Feb;288(3).
Edholm LD, Barrett D. High frequency behavior of the Leray transform: model hypersurfaces and projective duality. Indiana University Mathematics Journal. 2024 Nov;73(5):1833–1906.
Edholm LD, Chakrabarti D. Projections onto Lp-Bergman spaces of Reinhardt domains. Advances in Mathematics. 2024 Aug;451:109790. doi: 10.1016/j.aim.2024.109790
Edholm LD, Chakrabarti D, Bender C, Mainkar M. $L^p$ regularity of the Bergman projection on quotient domains. Canadian Journal of Mathematics. 2022 Jun;74(3):732-772. doi: 10.4153/S0008414X21000079
Edholm LD, Barrett D. The Leray transform: Factorization, dual CR structures, and model hypersurfaces in CP2. Advances in Mathematics. 2020 Apr 15;364:107012. doi: 10.1016/j.aim.2020.107012