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The Riesz transform of codimension smaller than one and the Wolff energy [electronic resource] / Benjamin Jaye, Fedor Nazorov, Maria Carmen Reguera, Xavier Tolsa

Author
Jaye, Benjamin, 1984-
Published
Providence, RI : American Mathematical Society, [2020]
Physical Description
v, 97 pages ; 26 cm
Additional Creators
Nazorov, Fedor (Fedya L'vovich), Reguera, Maria Carmen, 1981-, and Tolsa, Xavier
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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"--
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ISBN
9781470442132 (paperback)
9781470462499 (pdf)
Note
"Forthcoming, volume 266, number 1293."
Bibliography Note
Includes bibliographical references.
View MARC record | catkey: 35545355