Riesz transforms of non-integer homogeneity on uniformly disconnected\n sets

2014/02/13 by María Carmen Reguera, Xavier Tolsa, Reguera, Maria Carmen +1
Computer Science · Mathematics · #31C45 #42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1402.3104

openalex publication_date 2014/02/13 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain precise estimates for the L² norm of the\ns-dimensional Riesz transforms on very general measures supported on Cantor\nsets in mathbb R^d, with d-1<s<d. From these estimates we infer that, for\nthe so called uniformly disconnected compact sets, the capacity \γ_s\nassociated with the Riesz kernel x/|x|^s+1 is comparable to the capacity\n\C_{\(2)/(3)(d-s),\(3)/(2)} from non-linear potential theory.\n

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