The Riesz transform of codimension smaller than one and the Wolff energy
Author(s)
Bibliographic Information
The Riesz transform of codimension smaller than one and the Wolff energy
（Memoirs of the American Mathematical Society, no. 1293）
American Mathematical Society, c2020
Available at 7 libraries
Note
"July 2020, volume 266, number 1293 (third of 6 numbers)"
Includes bibliographical reference (p. 95-97)
Description and Table of Contents
Description
Fix $d\geq 2$, and $s\in (d-1,d)$. The authors characterize the non-negative locally finite non-atomic Borel measures $\mu $ in $\mathbb R^d$ for which the associated $s$-Riesz transform is bounded in $L^2(\mu )$ in terms of the Wolff energy. This extends the range of $s$ in which the Mateu-Prat-Verdera characterization of measures with bounded $s$-Riesz transform is known. As an application, the authors give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator $(-\Delta )^\alpha /2$, $\alpha \in (1,2)$, in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions.
by "Nielsen BookData"