中文摘要：

参数型Marcinkiewicz积分算子定义为：μρΩ（f）（x）=∫^∞0｜1/tρ∫｜x-y｜≤t｜Ω（x-y）/｜x-y｜^n-ρf（y）dy｜^2dt/t）1/2,其中Ω是零次齐次函数,且在单位球面上平均值为零.对于f∈BMO,证明了当Ω∈L（logL）γ（Sn-1）（γ〉2）以及某类Dini型条件时,[μρΩ（f）]2要么几乎处处无限要么几乎处处有限的,且当[μΩρ（f）]2几乎处处有限时,‖[μ^ρΩ（f）]^2‖BLO（R^n）≤C‖f‖2^BMO（Rn）.

英文摘要：

Higher-dimensional parameterized Marcinkiewicz integral operator is defined by μρΩ（f）（x）=∫^∞0｜1/tρ∫｜x-y｜≤t｜Ω（x-y）/｜x-y｜^n-ρf（y）dy｜^2dt/t）1/2 where Ω is homogeneous function of degree zero,with a mean value of zero on the unit sphere.When f∈BMO,It is proved that [μ^ρΩ（f）]^2 is either infinite everywhere or finite almost everywhere,furthermore if [μ^ρΩ（f）]^2 is finite almost everywhere,‖[μρΩ（f）]^2‖BLO（Rn）≤C‖f‖^2BMO（Rn）.