Jian-Guo Shi, Juan Wang, Meng Zhou, Bing Yin, Yan-Fang Shi
{"title":"齐次空间上奇异积分的多线性换易子端点学习","authors":"Jian-Guo Shi, Juan Wang, Meng Zhou, Bing Yin, Yan-Fang Shi","doi":"10.1109/ICMLC.2012.6359556","DOIUrl":null,"url":null,"abstract":"In this paper, we prove the endpoint estimates for the multilinear commutator related to the singular integral on the space of homogeneous type by means of the Lp (l <; p <; ∞) boundedness for the singular integral operator. The main tools of the proof are decomposition of function spaces and some general inequalities. The estimates we established are widely applied in support vector machines, especially the Minkowski's inequality and Holde's inequality which may have application to classification problems based on Kernel methods.","PeriodicalId":128006,"journal":{"name":"2012 International Conference on Machine Learning and Cybernetics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Endpoint learning for multilinear commutator of singular integral on space of homogeneous type\",\"authors\":\"Jian-Guo Shi, Juan Wang, Meng Zhou, Bing Yin, Yan-Fang Shi\",\"doi\":\"10.1109/ICMLC.2012.6359556\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we prove the endpoint estimates for the multilinear commutator related to the singular integral on the space of homogeneous type by means of the Lp (l <; p <; ∞) boundedness for the singular integral operator. The main tools of the proof are decomposition of function spaces and some general inequalities. The estimates we established are widely applied in support vector machines, especially the Minkowski's inequality and Holde's inequality which may have application to classification problems based on Kernel methods.\",\"PeriodicalId\":128006,\"journal\":{\"name\":\"2012 International Conference on Machine Learning and Cybernetics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 International Conference on Machine Learning and Cybernetics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICMLC.2012.6359556\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 International Conference on Machine Learning and Cybernetics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICMLC.2012.6359556","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Endpoint learning for multilinear commutator of singular integral on space of homogeneous type
In this paper, we prove the endpoint estimates for the multilinear commutator related to the singular integral on the space of homogeneous type by means of the Lp (l <; p <; ∞) boundedness for the singular integral operator. The main tools of the proof are decomposition of function spaces and some general inequalities. The estimates we established are widely applied in support vector machines, especially the Minkowski's inequality and Holde's inequality which may have application to classification problems based on Kernel methods.