非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.

Weighted Estimates for Fractional Type Marcinkiewicz Integral Operators on Non-homogeneous Spaces

Let (X, d, μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let M_β,ρ,q be the fractional type Marcinkiewicz integral operator on (X, d, μ). In this paper, for β ∈ 0, ∞), ρ ∈ (0, ∞) and q ∈ (1, ∞), under the assumption that M_β,ρ,q is bounded on L²(μ), the authors prove that M_β,ρ,q is bounded from the weighted Lebesgue space L^p(w) into the weighted weak Lebesgue space L^{p, ∞}(w) and from the weighted Morrey space L^p,κ,η(ω) into the weighted weak Morrey space WL^p,κ,η(ω).