Endpoint mixed weak type extrapolation

2023/01/25 by Sheldy Ombrosi, Ombrosi, Sheldy, Israel P. Rivera-Rı́os +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.10648

openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The purpose of this note is to extend the extrapolation result by by Cruz-Uribe Martell and Pérez as follows. Given a family F of pairs of functions suppose that for some 00, then, for every u∈ A₁ and every v∈ A_∞ we have that \Vert (f)/(v)\Vert_L^A,∞(uv)\lesssim\Vert (g)/(v)\Vert_L^A,∞(uv), where L^A,∞(uv)=inf\ λgt;0:sup_tgt;0A(t)w(\ x∈ℝ:|f(x)|gt;λt\ )≤1\ is the weak Orlicz type introduced by Iaffei. As a corollary of this extrapolation result we derive a mixed weak type inequality for Coifman-Rochberg-Weiss commutators.

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