Let μ be a Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ（B（x,r）） ≤ Urn for all x∈Rd, r 〉 0 and for some fixed 0 〈 n 〈 d. In this paper, under this assumption, we prove that 0-type Calder6n-Zygmund operator which is bounded on L2 （μ） is also bounded from L^∞（μ） into RBMO （μ） and from Hb （μ） into L1（μ）. According to the interpolation theorem introduced by Tolsa, the LP（μ）-boundedness （1 〈 p 〈 ∞） is established for θ-type Calder6n-Zygmund operators. Via a sharp maximal operator, it is shown that commutators and multilinear commutators of θ-type CMderθn-Zygmundoperator with RBMO （μ） function are bounded on LP（μ） （1 〈 p 〈 ∞）.
Let μΩ,b^m be the higher order commutator generated by Marcinkiewicz integral μΩ and a BMO（R^n） function b（x）. In this paper, we will study the continuity of μΩ and μΩ,b^m on homogeneous Morrey-Herz spaces.
In this paper,the boundedness for the multilinear commutators of Bochner-Riesz operator is considered.We prove that the multilinear commutators generated by Bochner-Riesz operator and Lipschitz function are bounded from Lp（Rn）into ∧˙（β-np）（Rn）and from Lnβ（Rn）into BMO（Rn）.
