Michael Penrod
University of Cincinnati
Title
Convex-set valued sparse operators in matrix weighted variable Lebesgue spaces
Abstract
In 2017, Nazarov, Petermichl, Treil, and Volberg introduced convex body-valued sparse operators to obtain estimates for the norms of Calder´on-Zygmund operators on matrix weighted L^2. In this talk, we combine four topics in harmonic analysis to give a new proof of bounds for Calderon-Zygmund operators on matrix weighted variable Lebesgue spaces. We combine tools from variable Lebesgue spaces, matrix weights, convex-set valued analysis, and the convex body-valued sparse operators mentioned above. With these tools, the proof is much simpler than the existing proof given by myself and Zoe Nieraeth in 2025.
This is joint work with Marcin Bownik, David Cruz-Uribe, and Fatih Sirin.