Seminario Análisis y Aplicaciones
Optimal Sparse Bounds and Commutator Characterizations Without Doubling
Ponente: Nathan Wanger (George Mason University)Fecha: viernes 22 de mayo de 2026 - 10:30Lugar: Aula Gris 1, ICMAT
Resumen:
We examine dyadic paraproducts and commutators in the non-homogeneous setting, where the underlying Borel measure μ is not assumed doubling. We first establish a pointwise sparse domination for dyadic paraproducts and related operators with symbols b ∈ BMO(μ), 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 < ∞, 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.
