03255nam 2200601 450 991081354820332120201204074241.01-4704-6249-4(CKB)4100000011437131(MiAaPQ)EBC6346626(RPAM)21684820(PPN)250799871(EXLCZ)99410000001143713120201204d2020 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierThe Riesz transform of codimension smaller than one and the Wolff energy /Benjamin Jaye [and three others]Providence, Rhode Island :American Mathematical Society,[2020]©20201 online resource (110 pages)Memoirs of the American Mathematical Society ;Number 1293"Forthcoming, volume 266, number 1293."1-4704-4213-2 Includes bibliographical references.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."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.Memoirs of the American Mathematical Society ;Number 1293.Harmonic analysisCalderón-Zygmund operatorLaplacian operatorLipschitz spacesPotential theory (Mathematics)Harmonic analysis.Calderón-Zygmund operator.Laplacian operator.Lipschitz spaces.Potential theory (Mathematics)515.7342B3731B15mscJaye Benjamin1984-1686961Nazorov Fedor(Fedya L'vovich),Reguera Maria Carmen1981-Tolsa XavierMiAaPQMiAaPQMiAaPQBOOK9910813548203321The Riesz transform of codimension smaller than one and the Wolff energy4060078UNINA