The Riesz transform of codimension smaller than one and the Wolff energy /

"Fix d [greater than or equal to] 2, and s [epsilon] (d - 1, d). We characterize the non-negative locally finite non-atomic Borel measures [mu] in Rd for which the associated s-Riesz transform is bounded in L²([mu]) in terms of the Wolff energy. This extends the range of s in which the Mateu-Pr...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Jaye, Benjamin, 1984- (Autor), Nazorov, Fedor (Fedya L'vovich) (Autor), Reguera, Maria Carmen, 1981- (Autor), Tolsa, Xavier (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, RI : American Mathematical Society, [2020]
Colección:Memoirs of the American Mathematical Society, number 1293
Temas:
Harmonic analysis.
Lipschitz spaces.
Laplacian operator.
Calderón-Zygmund operator.
Potential theory (Mathematics)
Potential theory (Physics)
Analyse harmonique.
Espaces de Lipschitz.
Laplacien.
Opérateur de Calderón-Zygmund.
Théorie du potentiel.
Análisis armónico
Potencial, Teoría del (Matemáticas)
Calderón-Zygmund operator
Harmonic analysis
Laplacian operator
Lipschitz spaces
Harmonic analysis on Euclidean spaces > Harmonic analysis in several variables {For automorphic theory, see mainly 11F30} > Harmonic analysis and PDE [See also 35-XX].
Potential theory {For probabilistic potential theory, see 60J45} > Higher-dimensional theory > Potentials and capacities, extremal length.
Acceso en línea:Texto completo
Descripción
Sumario:"Fix d [greater than or equal to] 2, and s [epsilon] (d - 1, d). We characterize the non-negative locally finite non-atomic Borel measures [mu] in Rd for which the associated s-Riesz transform is bounded in L²([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, we give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator ( -[delta])[infinity]/2, [infinity] [epsilon] (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"--
Notas:"Forthcoming, volume 266, number 1293."
Descripción Física:1 online resource (v, 110 pages)
Bibliografía:Includes bibliographical references.
ISBN:1470462494
9781470462499
ISSN:0065-9266 ;

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