2019/03/06 by Irina Holmes, Georgios Psaromiligkos, Holmes, Irina +3
Mathematics · #42B20 #42B35 #47A30 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #F.2.2 #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1903.02478
openalex publication_date 2019/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we give an example of measure satisfying the box condition on certain sub-bi-trees (see below) but not satisfying Carleson condition on those sub-bi-trees. This can be considered as a certain counterexample for two weight bi-parameter embedding of Carleson type. Our type of counterexample is impossible for a simple tree. In the case of a simple tree, the box condition, Carleson condition and two weight embedding are all equivalent. In the last section we show that bi-parameter box condition implies the bi-parameter capacitary estimate for dyadic rectangles.