(untitled) (Analysis in Theory and Applications, 2024)
The aim of this paper is to establish the boundedness of bilinear pseudo-differential operator T_σ and its commutator [b_1, b_2, T_σ] generated by T_σ and b_1, b_2∈ BMO(R^n) on generalized fractional weighted Morrey spaces L^p,η,φ (ω). Under assumption that a weight satisfies a certain condition, the authors prove that T_σ is bounded from products of spaces L^p_1,η_1,φ(ω_1)×L^p_2,η_2,φ(ω_2) into spaces L^p,η,φ (ω), where ω= (ω_1, ω_2) ∈ A_P , P = (p_1, p_2), η = η_1 + η_2 and 1p=1p_1+1p_2 with p_1, p_2 ∈ (1, ∞). Furthermore, the authors show that the [b_1, b_2, T_σ] is bounded from products of generalized fractional Morrey spaces L^p_1 ,η_1 ,φ (R^n)×L^p_2,η_2,φ (R^n) into L^p,η,φ(R^n). As corollaries, the boundedness of the T_σ and [b_1, b_2, T_σ] on generalized weighted Morrey spaces L^p,φ (ω) and on generalized Morrey spaces L^p,φ(R^n) is also obtained.