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 [pipe] · [pipe] is considered. The condition on α for which the Hardy-Littlewood maximal operator is bounded can be described completely.
| Original language | English |
|---|---|
| Pages (from-to) | 67-93 |
| Number of pages | 27 |
| Journal | Annales Academiae Scientiarum Fennicae Mathematica |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2020 |
Bibliographical note
Publisher Copyright:© Finnish Academy of Science and Letters.
Keywords
- Local morrey spaces of komori-shirai type
- Local morrey spaces of samko type
- Weights
ASJC Scopus subject areas
- General Mathematics
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