Titel: The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
Verlag: MP-AMM American Mathematical
Erscheinungsjahr: 2020
Sprache: Englisch
ISBN-10: 1470442132
ISBN-13: 9781470442132
Einband: PAP
Zustand: New
Gewicht: 580 Gramm

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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.

�ber die Autorin bzw. den Autor

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

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