Weighted local Morrey spaces
Weighted local Morrey spaces
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DOI：
10.5186/aasfm.2020.4504
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Shohei Nakamura;Y. Sawano;Hitoshi Tanaka
中科院分区：
文献类型：
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作者：
Shohei Nakamura;Y. Sawano;Hitoshi Tanaka
抽象的。讨论了线性算子和次线性算子在两类加权局部Morrey空间中的有界性。一种是娜塔莎·桑科在2008年定义的。另一种是由小森康夫和白井在2009年定义的。刻划了Hardy-Littlewood极大算子有界的权类。在一定的积分条件下，证明了奇异积分算子有界当且仅当Hardy-Littlewood极大算子有界。作为刻画的一个应用，考虑了加权函数|·|。在α上，Hardy-Littlewood极大算子有界的条件可以完全描述。
Abstract. We discuss the boundedness of linear and sublinear operators in two types of weighted local Morrey spaces. One is defined by Natasha Samko in 2008. The other is defined by Yasuo Komori-Furuya and Satoru Shirai in 2009. We characterize the class of weights for which the Hardy–Littlewood maximal operator is bounded. Under a certain integral condition it turns out that the singular integral operators are bounded if and only if the Hardy–Littlewood maximal operator is bounded. As an application of the characterization, the power weight function | · | is considered. The condition on α for which the Hardy–Littlewood maximal operator is bounded can be described completely.