2024/04/14 by Eduard Roure Perdices, Perdices, Eduard Roure
Mathematics · #42B25 (Primary) #46E30 (Secondary) #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2404.09351
openalex publication_date 2024/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a multi-variable extension of Rubio de Francia's restricted weak-type extrapolation theory that does not involve Rubio de Francia's iteration algorithm; instead, we rely on the following Sawyer-type inequality for the weighted Hardy-Littlewood maximal operator Mu: \Vert (Mu (fv))/(v) \VertL1,∞(uv) ≤ Cu,v \Vert f \VertL1(uv), u, uv ∈ A∞. Our approach can be adapted to recover weak-type A P extrapolation schemes, including an endpoint result that falls outside the classical theory. Among the applications of our work, we highlight extending outside the Banach range the well-known equivalence between restricted weak-type and weak-type for characteristic functions, and obtaining mixed and restricted weak-type bounds with Ap\mathcal R weights for relevant families of multi-variable operators, addressing the lack in the literature of these types of estimates. We also reveal several standalone properties of the class Ap\mathcal R.