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Algebra i Analiz, 2023 Volume 35, Issue 4, Pages 167–182 (Mi aa1877)

Research Papers

On Fourier multipliers with rapidly oscillating symbols

D. Stolyarov

Saint Petersburg State University

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

Keywords: Fourier multiplier, oscillatory integral.

Received: 18.10.2022


 English version:
St. Petersburg Mathematical Journal, 2024, 35:4, 719–729


© Steklov Math. Inst. of RAS, 2025