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arXiv · 1204.2135

The fractional Riesz transform and an exponential potential

Benjamin Jaye·Fedor Nazarov·Alexander Volberg
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Abstract

In this paper we study the $s$-dimensional Riesz transform of a finite measure $\mu$ in $\mathbf{R}^d$, with $s\in (d-1,d)$. We show that the boundedness of the Riesz transform of $\mu$ implies that a nonlinear potential of exponential type is finite $\mu$-almost everywhere. It appears to be the first result of this type for $s>1$.

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Benjamin Jaye, Fedor Nazarov, Alexander Volberg. 2012-04-10. The fractional Riesz transform and an exponential potential. https://arxiv.org/abs/1204.2135

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