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

Abstract

The aim of this paper is to establish the boundedness of the commutator [b1, b2, Tθ], which generated by the bilinear θ-type Calderon–Zygmund operators Tθ and the functions $$b_1, b_2 \in \widetilde {RBMO}(\mu)$$, 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 e-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 $${L^{{p_1}}}(\mu ) \times {L^{{p_2}}}(\mu )$$ with $$\frac{1}{p} = \frac{1}{{{p_1}}} + \frac{1}{{{p_2}}}(1 < p,{p_1},{p_2} < \infty )$$. Furthermore, the boundedness of the commutator [b1, b2, Tθ] on Morrey space $$M_p^q(\mu)$$ is also obtained, where 1 < q ≤ p < ∞.