Singular operators with antisymmetric kernels, related capacities, and Wolff potentials

2010/12/13 by David R. Adams, Adams, David R., Vladimir Eiderman +1
Mathematics · #30C85 (Secondary) #31B15 #31C45 #42B20 (Primary) #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #math.CA #msc:30C85 #msc:31B15 #msc:31C45 #msc:42B20

paper · pdf · doi:10.48550/arxiv.1012.2877

arxiv created 2010/12/13 · openalex publication_date 2010/12/13 · arxiv updated 2010/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a generalization of the Riesz operator in R^d and obtain estimates for its norm and for related capacities via the modified Wolff potential. These estimates are based on the certain version of T1 theorem for Calderón-Zygmund operators in metric spaces. We extend two versions of Calderón-Zygmund capacities in R^d to metric spaces and establish their equivalence (under certain conditions). As an application, we extend the known relations between s-Riesz capacities, 0<s<d, and the capacities in Nonlinear Potential Theory, to the case s=0.

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