Muckenhoupt-Wheeden conjectures for sparse operators

2016/09/13 by Cong Hoang, Kabe Moen, Hoang, Cong +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1609.03889

openalex publication_date 2016/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an example of a pair of weights (u,v) for which the Hardy-Littlewood maximal function is bounded from L^p(v) to L^p(u) and from L^p'(u^1-p') to L^p'(v^1-p') while a dyadic sparse operator is not bounded on the same domain and range. Our construction also provides an example of a single weight for which the weak-type endpoint does not hold for sparse operators.

Citations

• Some Maximal Inequalities

Related

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• On Muckenhoupt-Wheeden Conjecture
• Endpoint weak-type bounds beyond Calderón-Zygmund theory
• Zygmund type and flag type maximal functions, and sparse operators