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Record Nr. |
UNINA9910813548203321 |
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Autore |
Jaye Benjamin <1984-> |
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Titolo |
The Riesz transform of codimension smaller than one and the Wolff energy / / Benjamin Jaye [and three others] |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2020] |
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©2020 |
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ISBN |
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Descrizione fisica |
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1 online resource (110 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; Number 1293 |
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Classificazione |
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Disciplina |
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Soggetti |
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Harmonic analysis |
Calderón-Zygmund operator |
Laplacian operator |
Lipschitz spaces |
Potential theory (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Forthcoming, volume 266, number 1293." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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"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 |
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