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September 5, 2025Studia Mathematica0 citationsOpen Access

On some bilinear Fourier multipliers with oscillating factors, II

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TKTomoya KatoAMAkihiko MiyachiNSNaoto Shida

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. (2025) studied this question.

synapsesocial.com/papers/68bb4d206d6d5674bcd01063https://doi.org/10.4064/sm241227-12-3
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