Characterizations for the fractional maximal operator and its commutators on total Morrey spaces

IF 0.8 3区 数学 Q2 MATHEMATICS
V. S. Guliyev
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引用次数: 0

Abstract

We shall give a characterization for the strong and weak type Adams type boundedness of the fractional maximal operator \(M_{\alpha }\) on total Morrey spaces \(L^{p,\lambda ,\mu }(\mathbb {R}^n)\), respectively. Also we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator \(M_{b,\alpha }\) and commutator of fractional maximal operator \([b,M_{\alpha }]\) on \(L^{p,\lambda ,\mu }(\mathbb {R}^n)\) when b belongs to \(BMO(\mathbb {R}^n)\) spaces, whereby some new characterizations for certain subclasses of \(BMO(\mathbb {R}^n)\) spaces are obtained.

总莫里空间上分数最大算子及其换元子的特征
我们将分别给出总莫里空间 \(L^{p,\lambda ,\mu }(\mathbb {R}^n)\) 上分数最大算子 \(M_{\alpha }\) 的强型和弱型亚当斯类型有界性的特征。我们还给出了分数最大换向算子 \(M_{b,\alpha }\) 和分数最大算子 \([b,M_{\alpha }]\) 在 \(L^{p、当 b 属于 \(BMO(\mathbb {R}^n)\)空间时,在 \(L^{p, \mu }(\mathbb{R}^n)\)上的分数最大算子([b,M_{α}])和换元,从而得到了 \(BMO(\mathbb {R}^n)\)空间的某些子类的新特征。
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来源期刊
Positivity
Positivity 数学-数学
CiteScore
1.80
自引率
10.00%
发文量
88
审稿时长
>12 weeks
期刊介绍: The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.
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