English

On Fourier multipliers with rapidly oscillating symbols

Classical Analysis and ODEs 2022-04-19 v2

Abstract

We provide asymptotically sharp bounds for the LpL_p norms of the Fourier multipliers with the symbols eiλφ(ξ/ξ)e^{i\lambda \varphi(\xi/|\xi|)}, where λR\lambda\in \mathbb{R} is a large parameter.

Keywords

Cite

@article{arxiv.2203.04881,
  title  = {On Fourier multipliers with rapidly oscillating symbols},
  author = {Dmitriy Stolyarov},
  journal= {arXiv preprint arXiv:2203.04881},
  year   = {2022}
}

Comments

10 pages; second version contains the proofs of lower bounds for arbitrary d, some typos are also corrected