{"title":"广义dunkl型morrey空间中dunkl型分数阶积分算子的有界性","authors":"Y. Mammadov, S. Hasanli","doi":"10.12732/IJAM.V31I2.4","DOIUrl":null,"url":null,"abstract":"First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"11 1","pages":"211-230"},"PeriodicalIF":0.0000,"publicationDate":"2018-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"ON THE BOUNDEDNESS OF DUNKL-TYPE FRACTIONAL INTEGRAL OPERATOR IN THE GENERALIZED DUNKL-TYPE MORREY SPACES\",\"authors\":\"Y. Mammadov, S. Hasanli\",\"doi\":\"10.12732/IJAM.V31I2.4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35\",\"PeriodicalId\":14365,\"journal\":{\"name\":\"International journal of pure and applied mathematics\",\"volume\":\"11 1\",\"pages\":\"211-230\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of pure and applied mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/IJAM.V31I2.4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of pure and applied mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/IJAM.V31I2.4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
摘要
首先证明了dunkl型极大算子Mα在广义dunkl型Morrey空间Mp，ω，α上对1 < p <∞和从空间M1，ω，α到弱空间WM1，ω，α上是有界的。证明了dunkl型分数阶积分算子Iβ，α， 0 < β < 2α+ 2有界于广义dunkl型Morrey空间Mp，ω，α到Mq，ωp/q，α，其中β/(2α + 2) = 1/p−1/q, 1 < p < (2α+ 2)/β。学科分类:42B20、42B25、42B35
ON THE BOUNDEDNESS OF DUNKL-TYPE FRACTIONAL INTEGRAL OPERATOR IN THE GENERALIZED DUNKL-TYPE MORREY SPACES
First, we prove that the Dunkl-type maximal operator Mα is bounded on the generalized Dunkl-type Morrey spaces Mp,ω,α for 1 < p < ∞ and from the spaces M1,ω,α to the weak spaces WM1,ω,α. We prove that the Dunkl-type fractional order integral operator Iβ,α, 0 < β < 2α+ 2 is bounded from the generalized Dunkl-type Morrey spaces Mp,ω,α to Mq,ωp/q,α, where β/(2α + 2) = 1/p − 1/q, 1 < p < (2α+ 2)/β. AMS Subject Classification: 42B20, 42B25, 42B35
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