Year: 2022
Type: preprint
Abstract: We address $L^p(μ)\rightarrow L^p(λ)$ bounds for paraproducts in the Bloom setting. We introduce certain "sparse BMO" functions associated with sparse collections with no infinitely increasing chains, and use these to express sparse operators as sums of paraproducts and martingale transforms -- essentially, as Haar multipliers -- as well as to obtain an equivalence of norms between sparse operators $\mathcal{A}_\mathcal{S}$ and compositions of paraproducts $Π^*_aΠ_b$.
Source: arXiv (Cornell University)
Authors: Fragkiadaki, Valentia, Fay, Irina Holmes
Institution: Texas A&M University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4226420618