The Riesz Transform of Codimension Smaller Than One and the Wolff Energy - Couverture souple

Jaye, Benjamin; Nazarov, Fedor; Reguera, Maria Carmen; Tolsa, Xavier

Couverture souple

ISBN 10 : 1470442132 ISBN 13 : 9781470442132

Editeur : American Mathematical Society, 2020

Synopsis

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.

A propos du livre

À propos de l?auteur

Benjamin Jaye, Kent State University, OH

Fedor Nazarov, Kent State University, OH

Maria Carmen Reguera, University of Birmingham, UK

Xavier Tolsa, Institucio Catalana de Recerca i Estudis Avancats, Barcelona, Catalonia, Spain, and Universitat Autonoma de Barcelona, Catalonia, Spain

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 1470442132
• ISBN 13: 9781470442132
• Reliure: Broché
• Nombre de pages: 97
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible