The fractional Riesz transform and an exponential potential

Details The fractional Riesz transform and an exponential potential The fractional Riesz transform and an exponential potential

2012-04-10

arxiv.org/abs/1204.2135v1

Mathematics

Analysis of PDEs

48 pages, 2 figures

Scientific paper

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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