The Riesz Transform of Codimension Smaller Than One and the Wolff Energy PDF
by Benjamin Jaye
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.
Information
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Download - Immediately Available
- Format:PDF
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470462499
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Information
-
Download - Immediately Available
- Format:PDF
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:01/01/1900
- Category:
- ISBN:9781470462499