Amelia Stokolosa is a Ph.D. Student at UW-Madison, advised by Dr. Brian Street. Amelia is expected to graduate in May 2025.
In this talk, Amelia presents two different proofs of an inversion theorem for two classes of multi-parameter singular integrals that dates back to her first preprint in 2023.
(1) The original proof is based on PDE tools and an extension of a single-parameter a priori estimate by Christ and Geller from the 80s to the multi-parameter setting. (2) The more recent proof is based on Banach-algebraic tools. It relies on a more recent structural theorem Amelia proves, for which the key idea is the construction of a carefully constructed topology for two classes of multi-parameter singular integrals: product kernels and flag kernels. This latter work by Amelia simultaneously builds upon constructions by Christ, Geller, Glowacki, and Polin from 1992, and a more general class of multi-parameter singular integrals by Street from 2014.
Keywords: product kernel, flag kernel, non-isotropic homogeneity, multi-parameter singular integrals, inverse.
MSC2020: 43A85, 42B20 (Primary); 42B37 and 43A85 (Secondary).