A comparison principle for convolution measures with applications
| Autor: | Silva, Diogo Oliveira e, Quilodrán, René |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Math. Proc. Camb. Phil. Soc. 169 (2020) 307-322 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0305004119000197 |
| Popis: | We establish the general form of a geometric comparison principle for $n$-fold convolutions of certain singular measures in $\mathbb{R}^d$ which holds for arbitrary $n$ and $d$. This translates into a pointwise inequality between the convolutions of projection measure on the paraboloid and a perturbation thereof, and we use it to establish a new sharp Fourier extension inequality on a general convex perturbation of a parabola. Further applications of the comparison principle to sharp Fourier restriction theory are discussed in a companion paper. Comment: 17 pages, v2: updated reference to companion paper |
| Databáze: | arXiv |
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