This paper reveals boundedness criteria for bilinear fourier multipliers in Hörmander class, indicating key implications for operator theory.
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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Kato et al. (2025) studied this question.
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