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

Benjamin Jaye, Fedor Nazarov, Maria Carmen Reguera, Xavier Tolsa (Autoren)

Buch | Softcover

97 Seiten

2020
American Mathematical Society (Verlag)
978-1-4704-4213-2 (ISBN)

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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.

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

Erscheinungsdatum	02.07.2020
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	210 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-4213-2 / 1470442132
ISBN-13	978-1-4704-4213-2 / 9781470442132
Zustand	Neuware