- Nathan A. Wagner
- Assistant Professor
- Georgia Mason University
- Date: Nov. 12, Wednesday, 2025
- Time: 12:10pm -- 13:00pm
- Host: Bingyang Hu
- Room: Parker 328
- Abstract: We examine dyadic paraproducts and commutators in the non-homogeneous setting, where the underlying Borel measure \(\mu\) is not assumed doubling. We first establish a pointwise sparse domination for dyadic paraproducts and related operators with symbols \(b \in \mathrm{BMO}(\mu)\), improving upon a result of Lacey, where \(b\) satisfied a stronger Carleson-type condition coinciding with \(\mathrm{BMO}\) only in the doubling case. As an application, we derive sharpened weighted inequalities for the commutator of a dyadic Hilbert transform \(\mathcal{H}\) previously studied by Borges, Conde Alonso, Pipher, and Wagner. We also characterize the symbols for which \([\mathcal{H},b]\) is bounded on \(L^p(\mu)\) for \(1<p<\infty\), and provide examples showing that this symbol class lies strictly between those satisfying the \(p\)-Carleson packing condition and those belonging to martingale BMO. This talk is based on joint work with Francesco D'Emilio, Yongxi Lin, and Brett D. Wick.