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2011•arXiv (Cornell University)Open access

The $s$-Riesz transform of an $s$-dimensional measure in $\R^2$ is unbounded for $1

Vladimir Eiderman, Федор Леонидович Назаров, Alexander L'vovich Vol'berg

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Abstract

In this paper, we prove that for $s\in(1,2)$ there exists no totally lower irregular finite positive Borel measure $μ$ in $\R^2$ with\break $\mathcal H^s(\suppμ)

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What this paper is about

In this paper, we prove that for $s\in(1,2)$ there exists no totally lower irregular finite positive Borel measure $μ$ in $\R^2$ with\break $\mathcal H^s(\suppμ)

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Available abstract

In this paper, we prove that for $s\in(1,2)$ there exists no totally lower irregular finite positive Borel measure $μ$ in $\R^2$ with\break $\mathcal H^s(\suppμ)

Key concepts: Borel measure, Lebesgue measure, Measure (data warehouse), Integer (computer science), Mathematics, Combinatorics, Lebesgue integration, Discrete mathematics

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