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September 5, 2025Open Access

On some bilinear Fourier multipliers with oscillating factors, II

Key Points

The study establishes criteria for the boundedness of bilinear operators for various function spaces.
Operators are examined in contexts like L∞×L1 and L1×L∞, demonstrating different boundedness results.
The consideration of oscillating factors adds depth to the analysis of bilinear fourier multipliers.
Applications of these findings extend to operator theory and harmonic analysis in mathematical research.

Abstract

For s>0, s≠1, bilinear Fourier multipliers of the form ei(∣∣ξ∣∣s+∣∣η∣∣s+∣∣ξ+η∣∣s)σ(ξ,η) are considered, where σ(ξ,η) belongs to the Hörmander class Sm1,0(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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Cite This Study

Kato et al. (Sat,) studied this question.

synapsesocial.com/papers/68bb4d206d6d5674bcd01063 https://doi.org/https://doi.org/10.4064/sm241227-12-3

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