A comparison principle for convolution measures with applications
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.10463
- arXiv:
- arXiv:1804.10463
- Bibcode:
- 2018arXiv180410463S
- Keywords:
-
- Mathematics - Classical Analysis and ODEs
- E-Print:
- 17 pages, v2: updated reference to companion paper