Beyond Local Maximal Operators

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• 作者：Hannes Luiro ; Antti V. Vähäkangas
• 关键词：Local maximal operator ; Muckenhoupt weight ; Fractional Sobolev space
• 刊名：Potential Analysis
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：46
• 期：2
• 页码：201-226
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Potential Theory; Probability Theory and Stochastic Processes; Geometry; Functional Analysis;
• 出版者：Springer Netherlands
• ISSN：1572-929X
• 卷排序：46

文摘

We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions.