On some bilinear Fourier multipliers with oscillating factors, II

2024/12/28 by Tomoya Kato, Kato, Tomoya, Akihiko Miyachi +5
Mathematics · #42B15 #42B20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2412.20010

openalex publication_date 2024/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For s > 0, s ≠ 1, bilinear Fourier multipliers of the form e^{i (|ξ|s + |η|s+ |ξ+ η|s)} σ(ξ, η) are considered, where σ(ξ, η) belongs to the Hörmander class S^m_{1, 0}(ℝ²ⁿ). A criterion for m to ensure the L^∞× L^∞ → L^∞, L¹ × L^∞ → L¹, and L^∞ × L¹ → L¹ boundedness of the corresponding bilinear operators is given.

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