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非齐型空间上分数型Marcinkiewicz积分算子的加权估计

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非齐型空间上分数型Marcinkiewicz积分算子的加权估计 林海波, 王宸雁中国农业大学理学院 北京 100083 Weighted Estimates for Fractional Type Marcinkiewicz Integral Operators on Non-homogeneous Spaces Hai Bo LIN, Chen Yan WANGCollege of Science, China Agricultural University, Beijing 100083, P. R. China
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摘要令(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Mβ,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Mβ,ρ,qL2μ)上有界,则Mβ,ρ,q是从加权Lebesgue空间Lpw)到加权弱Lebesgue空间Lp,∞w)上有界和从加权Morrey空间Lp,κ,ηω)到加权弱Morrey空间WLp,κ,ηω)上有界.
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收稿日期: 2019-08-14
MR (2010):O177.2
基金资助:国家自然科学基金资助项目(11471042)
通讯作者:王宸雁E-mail: chenyanwangcau@126.com
作者简介: 林海波,E-mail:haibolincau@126.com
引用本文:
林海波, 王宸雁. 非齐型空间上分数型Marcinkiewicz积分算子的加权估计[J]. 数学学报, 2020, 63(5): 443-464. Hai Bo LIN, Chen Yan WANG. Weighted Estimates for Fractional Type Marcinkiewicz Integral Operators on Non-homogeneous Spaces. Acta Mathematica Sinica, Chinese Series, 2020, 63(5): 443-464.
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http://www.actamath.com/Jwk_sxxb_cn/CN/ http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I5/443


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