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 and harmonic analysis. 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.
Preprints (submitted)
Preprints (accepted)
Publications
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
Edholm LD, McNeal JD. Sobolev Mapping of Some Holomorphic Projections. The Journal of Geometric Analysis. 2020 Apr;30(2):1293–1311. doi: 10.1007/s12220-019-00345-6
Edholm LD, McNeal JD, Chakrabarti D. Duality and approximation of Bergman spaces. Advances in Mathematics. 2019 Jan 7;341(7):616-656. doi: 10.1016/j.aim.2018.10.041
Edholm LD, McNeal JD. Bergman Subspaces and Subkernels: Degenerate L-p Mapping and Zeroes. The Journal of Geometric Analysis. 2017 Oct;27(4):2658–2683. doi: 10.1007/s12220-017-9777-4