{"title":"Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes","authors":"N. Tumalun, H. Gunawan","doi":"10.22342/JIMS.25.3.817.203-209","DOIUrl":null,"url":null,"abstract":"In this paper, we show that the Morrey spaces $ L^{1,\\left( \\frac{\\lambda}{p} -\\frac{n}{p} + n \\right) } \\left( \\mathbb{R}^{n} \\right) $ are embedded betweenweak Morrey spaces $ wL^{p,\\lambda}\\left( \\mathbb{R}^{n} \\right) $ and Stummelclasses $ S_{\\alpha}\\left( \\mathbb{R}^{n} \\right) $ under some conditions on$ p, \\lambda $ and $ \\alpha $. More precisely, we prove that $ wL^{p,\\lambda}\\left(\\mathbb{R}^{n} \\right) \\subseteq L^{1,\\left( \\frac{\\lambda}{p} - \\frac{n}{p} + n\\right) } \\left( \\mathbb{R}^{n} \\right) \\subseteq S_{\\alpha}\\left( \\mathbb{R}^{n}\\right) $ where $ 1p\\infty, 0\\lambdan $ and $ \\frac{n-\\lambda}{p}\\alphan $.We also show that these inclusion relations under the above conditions are proper.Lastly, we present an inequality of Adams' type \\cite{A}","PeriodicalId":42206,"journal":{"name":"Journal of the Indonesian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indonesian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22342/JIMS.25.3.817.203-209","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 11
Abstract
In this paper, we show that the Morrey spaces $ L^{1,\left( \frac{\lambda}{p} -\frac{n}{p} + n \right) } \left( \mathbb{R}^{n} \right) $ are embedded betweenweak Morrey spaces $ wL^{p,\lambda}\left( \mathbb{R}^{n} \right) $ and Stummelclasses $ S_{\alpha}\left( \mathbb{R}^{n} \right) $ under some conditions on$ p, \lambda $ and $ \alpha $. More precisely, we prove that $ wL^{p,\lambda}\left(\mathbb{R}^{n} \right) \subseteq L^{1,\left( \frac{\lambda}{p} - \frac{n}{p} + n\right) } \left( \mathbb{R}^{n} \right) \subseteq S_{\alpha}\left( \mathbb{R}^{n}\right) $ where $ 1p\infty, 0\lambdan $ and $ \frac{n-\lambda}{p}\alphan $.We also show that these inclusion relations under the above conditions are proper.Lastly, we present an inequality of Adams' type \cite{A}