{"title":"Morrey空间嵌入在弱Morrey空间和Stummel类之间","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":"{\"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}","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}
Morrey Spaces are Embedded Between Weak Morrey Spaces and Stummel Classes
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}