The Riesz transform of codimension smaller than one and the Wolff energy / / Benjamin Jaye [and three others]
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| Autore: |
Jaye Benjamin <1984->
|
| Titolo: |
The Riesz transform of codimension smaller than one and the Wolff energy / / Benjamin Jaye [and three others]
|
| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , [2020] |
| ©2020 | |
| Descrizione fisica: | 1 online resource (110 pages) |
| Disciplina: | 515.73 |
| Soggetto topico: | Harmonic analysis |
| Calderón-Zygmund operator | |
| Laplacian operator | |
| Lipschitz spaces | |
| Potential theory (Mathematics) | |
| Classificazione: | 42B3731B15 |
| Persona (resp. second.): | NazorovFedor (Fedya L'vovich) |
| RegueraMaria Carmen <1981-> | |
| TolsaXavier | |
| Note generali: | "Forthcoming, volume 266, number 1293." |
| Nota di bibliografia: | Includes bibliographical references. |
| Nota di contenuto: | The general scheme : finding a large Lipschitz oscillation coefficient -- Upward and downward domination -- Preliminary results regarding reflectionless measures -- The basic energy estimates -- Blow up I : The density drop -- The choice of the shell -- Blow up II : doing away with [epsilon] -- Localization around the shell -- The scheme -- Suppressed kernels -- Step I : Calderón-Zygmund theory (from a distribution to an Lp-function) -- Step II : The smoothing operation -- Step III : The variational argument -- Contradiction. |
| Sommario/riassunto: | "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"-- |
| Titolo autorizzato: | The Riesz transform of codimension smaller than one and the Wolff energy |
| ISBN: | 1-4704-6249-4 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910813548203321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Memoirs of the American Mathematical Society ; ; Number 1293.