【摘要】 研究了下述广义Marcinkiewicz积分算子μΩ,αf(x)=∫∞0|∫|x-y|≤tΩ(x-y)|x-y|n-1f(y)dy|2dtt3+2α12当零次齐次函数Ω∈Hq(Sn-1),q=n-1n-1+α,α≥0,且满足一定的消失性,则对于任意的1<p<∞,算子μΩ,α是L.pα到Lp有界的.同时证明,当2≤p<∞时,相应于g*λ函数和面积积分函数的Marcinkiewicz积分算子μ*Ω,λ,α,μΩ,S,α的L.pα到Lp的有界性.更多还原

【Abstract】 The following Marcinkiewicz integral operator is investigatedμ_Ω,αf（x）=∫^∞₀∫_|x-y|≤tΩ（x-y）|x-y|^n-1f（y）dy²dtt^3+2α12,where Ω∈H^q(S^n-1),q=n-1n-1+α,α≥0, satisfying certain cancellation conditions. The boundedness of operators μ_Ω,α,μ^*_Ω,λ,α　and μ_Ω,S,α is proved.更多还原