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We obtain the boundedness of a commutator generated by multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents.

A group G is said to be conjugacy separable if for each pair of elements x y ∈ G such that x and y are not conjugate in G, there exists a finite homomorphic imagē G of G such that the images of x y are not conjugate inḠ. In this note, we show that the tree products of finitely many conjugacy separable and subgroup separable groups amalgamating central subgroups with trivial intersections are conjugacy separable. We then apply our results to polycyclic-by-finite groups and free-by-finite groups.

In this paper, we study the boundedness of commutator[b,T]of Riesz transform associated with Schrödinger operator andbisBMOtype function, note that the kernel ofThas no smoothness, and the boundedness fromHb1(Rn)→L1(Rn)is obtained.