On extremizing sequences for the adjoint restriction inequality on the cone
| Autor: | René Quilodrán |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics 16. Peace & justice 01 natural sciences Closed and exact differential forms 03 medical and health sciences symbols.namesake Mathematics - Analysis of PDEs 0302 clinical medicine Fourier transform Cone (topology) Mathematics - Classical Analysis and ODEs Homogeneous space symbols 030212 general & internal medicine 0101 mathematics Mathematics |
| Zdroj: | Journal of the London Mathematical Society. 87:223-246 |
| ISSN: | 0024-6107 |
| DOI: | 10.1112/jlms/jds046 |
| Popis: | It is known that extremizers for the $L^2$ to $L^6$ adjoint Fourier restriction inequality on the cone in $\mathbb{R}^3$ exist. Here we show that nonnegative extremizing sequences are precompact, after the application of symmetries of the cone. If we use the knowledge of the exact form of the extremizers, as found by Carneiro, then we can show that nonnegative extremizing sequences converge, after the application of symmetries. Comment: 27 pages. Includes referee comments |
| Databáze: | OpenAIRE |
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