{"title":"Orlicz空间中弱紧集的例子","authors":"D. Dauitbek, Y. Nessipbayev, K. Tulenov","doi":"10.31489/2022m2/72-82","DOIUrl":null,"url":null,"abstract":"This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space LΦ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Examples of weakly compact sets in Orlicz spaces\",\"authors\":\"D. Dauitbek, Y. Nessipbayev, K. Tulenov\",\"doi\":\"10.31489/2022m2/72-82\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space LΦ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.\",\"PeriodicalId\":29915,\"journal\":{\"name\":\"Bulletin of the Karaganda University-Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Karaganda University-Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31489/2022m2/72-82\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Karaganda University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31489/2022m2/72-82","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
This paper provides a number of examples of relatively weakly compact sets in Orlicz spaces. We show some results arising from these examples. Particularly, we provide a criterion which ensures that some Orlicz function is increasing more rapidly than another (in a sense of T. Ando). In addition, we point out that if a bounded subset K of the Orlicz space LΦ is not bounded by the modular Φ, then it is possible for a set K to remain unbounded under any modular Ψ increasing more rapidly than Φ.
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