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100   $a20201204d2020      uy             0
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 14$aThe Riesz transform of codimension smaller than one and the Wolff energy /$fBenjamin Jaye [and three others]
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2020]
210  4$d©2020
215   $a1 online resource (110 pages)
225 1 $aMemoirs of the American Mathematical Society ;$vNumber 1293
300   $a"Forthcoming, volume 266, number 1293."
311   $a1-4704-4213-2 
320   $aIncludes bibliographical references.
327   $aThe 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 : Caldero?n-Zygmund theory (from a distribution to an Lp-function) -- Step II : The smoothing operation -- Step III : The variational argument -- Contradiction.
330   $a"Fix d [greater than or equal to] 2, and s [epsilon] (d - 1, d). We characterize the non-negative locally finite non-atomic Borel measures [mu] in Rd for which the associated s-Riesz transform is bounded in L²([mu]) in terms of the Wolff energy. This extends the range of s in which the Mateu-Prat-Verdera characterization of measures with bounded s-Riesz transform is known. As an application, we give a metric characterization of the removable sets for locally Lipschitz continuous solutions of the fractional Laplacian operator (-[delta])[infinity]/2, [infinity] [epsilon] (1, 2), in terms of a well-known capacity from non-linear potential theory. This result contrasts sharply with removability results for Lipschitz harmonic functions"--$cProvided by publisher.
410  0$aMemoirs of the American Mathematical Society ;$vNumber 1293.
606   $aHarmonic analysis
606   $aCaldero?n-Zygmund operator
606   $aLaplacian operator
606   $aLipschitz spaces
606   $aPotential theory (Mathematics)
615  0$aHarmonic analysis.
615  0$aCaldero?n-Zygmund operator.
615  0$aLaplacian operator.
615  0$aLipschitz spaces.
615  0$aPotential theory (Mathematics)
676   $a515.73
686   $a42B37$a31B15$2msc
700   $aJaye$b Benjamin$f1984-$01539881
702   $aNazorov$b Fedor$g(Fedya L'vovich),
702   $aReguera$b Maria Carmen$f1981-
702   $aTolsa$b Xavier
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910794335703321
996   $aThe Riesz transform of codimension smaller than one and the Wolff energy$93791058
997   $aUNINA