The Riesz transform of codimension smaller than one and the Wolff energy / Benjamin Jaye, Fedor Nazorov, Maria Carmen Reguera, Xavier Tolsa.
| Author/creator | Jaye, Benjamin, 1984- |
| Other author | Nazorov, Fedor (Fedya L'vovich) |
| Other author | Reguera, Maria Carmen, 1981- |
| Other author | Tolsa, Xavier. |
| Format | Electronic |
| Publication Info | Providence, RI : American Mathematical Society, [2020] |
| Description | v, 97 pages ; 26 cm |
| Supplemental Content | Full text available from Ebook Central - Academic Complete |
| Subjects |
| 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. |
| Abstract | "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. |
| General note | "Forthcoming, volume 266, number 1293." |
| Bibliography note | Includes bibliographical references. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2020032234 |
| ISBN | 9781470442132 (paperback) |
| ISBN | (pdf) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |