On Fourier multipliers with rapidly oscillating symbols

preprint2022arXivOpen access

Abstract

We provide asymptotically sharp bounds for the LpL_p norms of the Fourier multipliers with the symbols eiλφ(ξ/∣ξ∣)e^{iλφ(ξ/|ξ|)}, where λ∈Rλ\in \mathbb{R} is a large parameter.

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