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Author Jaye, Benjamin, 1984- author.

Title The Riesz transform of codimension smaller than one and the Wolff energy / Benjamin Jaye, Fedor Nazorov, Maria Carmen Reguera, Xavier Tolsa
Published Providence, RI : American Mathematical Society, [2020]
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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 Print version record
Subject Calderón-Zygmund operator.
Harmonic analysis.
Laplacian operator.
Lipschitz spaces.
Potential theory (Mathematics)
Calderón-Zygmund operator
Harmonic analysis on Euclidean spaces -- Harmonic analysis in several variables {For automorphic theory, see mainly 11F30} -- Harmonic analysis and PDE [See also 35-XX].
Harmonic analysis
Laplacian operator
Lipschitz spaces
Potential theory (Mathematics)
Potential theory {For probabilistic potential theory, see 60J45} -- Higher-dimensional theory -- Potentials and capacities, extremal length.
Form Electronic book
Author Nazorov, Fedor (Fedya L'vovich), author.
Reguera, Maria Carmen, 1981- author.
Tolsa, Xavier, author.
ISBN 1470462494
9781470462499