Riesz Transform of Codimension Smaller Than One and the Wolff Energy (eBook)

Benjamin Jaye (Autor)

eBook Download: PDF

97 Seiten
American Mathematical Society (Verlag)
978-1-4704-6249-9 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• ISBN-10: 1-4704-6249-4 / 1470462494
• ISBN-13: 978-1-4704-6249-9 / 9781470462499