Commutators of Bilinear θ-Type Calderón–Zygmund Operators on Morrey Spaces Over Non-Homogeneous Spaces

The aim of this paper is to establish the boundedness of the commutator [b1, b2, Tθ], which generated by the bilinear θ-type Calderón–Zygmund operators Tθ and the functions b1,b2∈RBMO~(μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b_1, b_2 \in \widetilde {RBMO}(\mu)$$\end{document}, on non-homogeneous metric measure space satisfying the so-called geometrically doubling and the upper doubling conditions. Under the assumption that the dominating function λ satisfies the ε-weak reverse doubling conditions, the author proves that the commutator [b1, b2, Tθ] is bounded from the Lebesgue space Lp(μ) into the product of Lebesgue space Lp1(μ)×Lp2(μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L^{{p_1}}}(\mu ) \times {L^{{p_2}}}(\mu )$$\end{document} with 1p=1p1+1p2(1<p,p1,p2<∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{p} = \frac{1}{{{p_1}}} + \frac{1}{{{p_2}}}(1 < p,{p_1},{p_2} < \infty )$$\end{document}. Furthermore, the boundedness of the commutator [b1, b2, Tθ] on Morrey space Mpq(μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_p^q(\mu)$$\end{document} is also obtained, where 1 < q ≤ p < ∞.