| Description |
1 online resource (v, 110 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 1293 |
| Contents |
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 |
| Summary |
"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"-- Provided by publisher |
| Notes |
"Forthcoming, volume 266, number 1293." |
| Bibliography |
Includes bibliographical references |
| Notes |
Description based on print version record |
| Subject |
Harmonic analysis.
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Lipschitz spaces.
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Laplacian operator.
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Calderón-Zygmund operator.
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Potential theory (Mathematics)
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Potential theory (Physics)
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Análisis armónico
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Potencial, Teoría del (Matemáticas)
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Potential theory (Physics)
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Calderón-Zygmund operator
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Harmonic analysis
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Laplacian operator
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Lipschitz spaces
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Potential theory (Mathematics)
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Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables {For automorphic theory, see mainly 11F30} -- Harmonic analysis and PDE [See also 35-XX].
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Potential theory {For probabilistic potential theory, see 60J45} -- Higher-dimensional theory -- Potentials and capacities, extremal length.
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| Form |
Electronic book
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| Author |
Nazorov, Fedor (Fedya L'vovich), author.
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Reguera, Maria Carmen, 1981- author.
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Tolsa, Xavier, author.
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| ISBN |
1470462494 |
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9781470462499 |
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