具有Besov正则性的双线性双参数Fourier乘子的加权估计

Weighted Estimates for Bilinear and Bi-Parameter Fourier Multipliers with Besov Regularity

摘要: 本文研究了满足Besov正则性条件的双线性双参数Fourier乘子，建立了对应算子的加权范数不等式。文中使用了二进制单位分解构造尺度截断乘子，结合Littlewood-Paley理论，证明了该类乘子算子在加权的$L^p$ 空间上的有界性，完善了双参数框架下的Hörmander型乘子理论。

Abstract: This paper investigates bilinear and bi-parameter Fourier multipliers satisfying the Besov regularity conditions and establishes the weighted norm inequality for the corresponding multiplier operators. By using the dyadic partition of unity to construct scale-truncated multipliers and combined with the Littlewood-Paley theory, we prove the boundedness of such multiplier operators on weighted $L^p$ spaces. The results presented in this paper improve the Hörmander type multiplier theorems in the bi-parameter setting.