粗糙算子在Morrey空间上的一个Sobolev型不等式
A Sobolev-Type Inequality for Rough Operators on the Morrey Space
DOI: 10.12677/AAM.2026.154162, PDF,    国家自然科学基金支持
作者: 周辰泽：西北师范大学数学与统计学院，甘肃 兰州
关键词: 极大函数；点态估计；Morrey空间；Sobolev型不等式；Maximum Function； Point State Estimation； Morrey Space； Sobolev-Type Inequality
摘要: 主要研究粗糙奇异积分算子在Morrey空间上的Sobolev 型不等式.利用Hardy-Littlewood极 大函数的点态不等式和Morrey空间中的有界性，得到了粗糙奇异积分算子在Morrey空间上的 一个由梯度范数控制的 Sobolev型不等式.
Abstract: The main goal of this paper focuses on the Sobolev-type inequalities of Rough Singular Integral Operator in the Morrey space. By using the pointwise inequality of the Hardy- Littlewood maximal function and the boundedness in the Morrey space, a Sobolev- type inequality controlled by the gradient norm for Rough Singular Integral Operator is obtained on the Morrey space.
文章引用：周辰泽. 粗糙算子在Morrey空间上的一个Sobolev型不等式[J]. 应用数学进展, 2026, 15(4): 341-346. https://doi.org/10.12677/AAM.2026.154162

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