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| 摘要: |
| 本文研究了单边 Hardy-Littlewood 极小算子的上半连续性及单边 Hardy-Littlewood 极大算子的下半连续性问题.利用半连续性的相关性质和新型集合测度估计等获得了单边 Hardy-Littlewood 极小算子 $m^{+}f(x)$ 在 $\mathbb{R}^{n}$ 上的上半连续性和单边 Hardy-Littlewood 极大算子 $M^{+}f(x)$ 在 $\mathbb{R}^{n}$ 上的下半连续性,推广了 Hardy-Littlewood 极大算子的半连续性成果. |
| 关键词: 单边极小算子 单边极大算子 上半连续 下半连续 |
| DOI： |
| 分类号:O174.3 |
| 基金项目:国家自然科学基金资助(11401175);河南省自然科学基金资助(202300410184);河南省教育厅高等学校重点科研项目(19A110017);河南省高校基本科研业务费专项(NSFRF200329). |
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| THE SEMI-CONTINUITY FOR TWO KINDS OF ONE-SIDED OPERATORS |
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WANG Ling
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| Abstract: |
| In this paper, the upper and lower semi-continuities for one-sided Hardy-Littlewood minimum operators and one-sided Hardy-Littlewood maximal operators are studied respectively. By using the properties of semi-continuity and a new type measure estimates for sets on $\mathbb{R}^{n}$, the upper semi-continuity of the one-sided minimum function $m^{+}f(x)$ and the lower semi-continuity of the one-sided maximal operators $M^{+}f(x)$ on $\mathbb{R}^{n}$ are obtained. These results generalize the semi-continuity of Hardy-Littlewood maximal operators.In this paper, the upper and lower semi-continuities for one-sided Hardy-Littlewood minimum operators and one-sided Hardy-Littlewood maximal operators are studied respectively. By using the properties of semi-continuity and a new type measure estimates for sets on $\mathbb{R}^{n}$, the upper semi-continuity of the one-sided minimum function $m^{+}f(x)$ and the lower semi-continuity of the one-sided maximal operators $M^{+}f(x)$ on $\mathbb{R}^{n}$ are obtained. These results generalize the semi-continuity of Hardy-Littlewood maximal operators. |
| Key words: one-sided minimum operator one-sided maximal operator upper semicontinuity lower semi-continuity |
