On the Luzin N-property and the uncertainty principle for Sobolev mappings
| Autor: | Mikhail V. Korobkov, Alba Roviello, Adele Ferone |
|---|---|
| Přispěvatelé: | Ferone, Adele, Korobkov, Mikhail V., Roviello, Alba |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Class (set theory) Uncertainty principle 01 natural sciences Hausdorff measure 46E30 Lorentz space 0103 physical sciences 46E35 fractional Sobolev classes 0101 mathematics Luzin $N\mskip-2mu$-property Mathematics Morse–Sard theorem Numerical Analysis Applied Mathematics 010102 general mathematics 58C25 Sobolev–Lorentz mappings Critical value Sobolev space Luzin N property 010307 mathematical physics Analysis 26B35 |
| Zdroj: | Anal. PDE 12, no. 5 (2019), 1149-1175 |
| ISSN: | 1149-1175 |
| Popis: | We say that a mapping [math] satisfies the [math] - [math] -property if [math] whenever [math] , where [math] means the Hausdorff measure. We prove that every mapping [math] of Sobolev class [math] with [math] satisfies the [math] - [math] -property for every [math] with ¶ [math] ¶ We prove also that for [math] and for the critical value [math] the corresponding [math] - [math] -property fails in general. Nevertheless, this [math] - [math] -property holds for [math] if we assume in addition that the highest derivatives [math] belong to the Lorentz space [math] instead of [math] . ¶ We extend these results to the case of fractional Sobolev spaces as well. Also, we establish some Fubini-type theorems for [math] -Nproperties and discuss their applications to the Morse–Sard theorem and its recent extensions. |
| Databáze: | OpenAIRE |
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