The Riesz Transform of Codimension Smaller Than One and the Wolff Energy Paperback / softback
by Benjamin Jaye, Fedor Nazarov, Maria Carmen Reguera, Xavier Tolsa
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
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
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2020
- Category:
- ISBN:9781470442132
Other Formats
- PDF from £76.50
Information
-
Available to Order - This title is available to order, with delivery expected within 2 weeks
- Format:Paperback / softback
- Pages:97 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2020
- Category:
- ISBN:9781470442132