{"title":"Lipschitz空间及其周围的紧性","authors":"J. Gulgowski, P. Kasprzak, Piotr Ma'ckowiak","doi":"10.4064/sm221020-16-3","DOIUrl":null,"url":null,"abstract":"The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\\\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.","PeriodicalId":51179,"journal":{"name":"Studia Mathematica","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Compactness in Lipschitz spaces and around\",\"authors\":\"J. Gulgowski, P. Kasprzak, Piotr Ma'ckowiak\",\"doi\":\"10.4064/sm221020-16-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\\\\\\\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.\",\"PeriodicalId\":51179,\"journal\":{\"name\":\"Studia Mathematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4064/sm221020-16-3\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm221020-16-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The aim of the paper is to characterize (pre)compactness in the spaces of Lipschitz/H\"older continuous mappings acting from a compact metric space to a normed space. To this end some extensions and generalizations of already existing compactness criteria for the spaces of bounded and continuous mappings with values in normed spaces needed to be established. Those auxiliary results, which are interesting on their own since they use a concept of equicontinuity not seen in the literature, are based on an abstract compactness criterion related to the recently introduced notion of an equinormed set.
期刊介绍：
The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
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