Nathan Wagner (George Mason U.) - Optimal Sparse Bounds and Commutator Characterizations Without D.. скачать в хорошем качестве

Nathan Wagner (George Mason U.) - Optimal Sparse Bounds and Commutator Characterizations Without D..

Nathan Wagner (George Mason University) - Optimal Sparse Bounds and Commutator Characterizations Without Doubling Recorded talk on Nov 18, 2025 at the Online Analysis Research Seminar (OARS) 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 BMO(\mu), improving upon a result of Lacey, where b satisfied a stronger Carleson-type condition coinciding with BMO only in the doubling case. As an application, we derive sharpened weighted inequalities for the commutator of a dyadic Hilbert transform H previously studied by Borges, Conde Alonso, Pipher, and Wagner. We also characterize the symbols for which [H,b] is bounded on L^p 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. https://sites.google.com/view/o-a-r-s