DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Nathan Wagner (Georgia Mason University)

Title: Optimal sparse bounds and commutator characterizations without doubling

Abstract: 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 \(L^p(μ)\) 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.

For more details, please visit https://webhome.auburn.edu/~lzc0090/SASA/20251112_Wagner.html