On oscillatory integrals with H\"older phases
Dynamical Systems
2022-11-17 v1 Classical Analysis and ODEs
Abstract
We exhibit a family of autosimilar H\"older maps that satisfies a fractal version of the Van Der Corput Lemma, despite not being absolutely continuous. The result is a direct consequence of a recent work of Sahlsten and Steven arXiv:2009.01703, which is based on a powerful theorem of Bourgain known as a sum-product phenomenon estimate. We give a substantially simpler proof of this fact in our particular context, using an elementary method inspired from arXiv:1704.02909 to check the non-concentration estimates that are needed to apply the sum-product phenomenon. This method allows us to gain additional control over the decay rate.
Keywords
Cite
@article{arxiv.2211.08088,
title = {On oscillatory integrals with H\"older phases},
author = {Gaétan Leclerc},
journal= {arXiv preprint arXiv:2211.08088},
year = {2022}
}
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15 pages