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 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 July 2024)
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Preprints (submitted)
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Preprints (accepted)
Publications
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
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