{"title":"广义大维纳汞齐空间和哈代-利特尔伍德最大算子的有界性","authors":"A. Turan Gürkanlı","doi":"arxiv-2408.02406","DOIUrl":null,"url":null,"abstract":"Let $1<p,q<\\infty$ and let $a(x), b(x)$ be weight functions. In the present\npaper we define and investigate some basic properties of generalized grand\nWiener amalgam space $W( L^{p),\\theta_1}(\\mathbb R^{n})),\nL^{q),\\theta_2}(\\mathbb R^{n})),$ where generalized grand Lebesgue spaces\n$L_{a}^{p)}(\\mathbb R^{n})$ and $L_{b}^{q)}(\\mathbb R^{n}),$ are local and\nglobal components, respectively. Next we study embeddings for these spaces,\nalso we give some more properties of these spaces. At the end of this work, we\ndiscuss boundedness and unboundedness of the Hardy-Littlewood maximal operator\nbetween some generalized grand Wiener amalgam spaces.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Generalized Grand Wiener Amalgam Spaces and the boundedness of Hardy-Littlewood maximal operators\",\"authors\":\"A. Turan Gürkanlı\",\"doi\":\"arxiv-2408.02406\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $1<p,q<\\\\infty$ and let $a(x), b(x)$ be weight functions. In the present\\npaper we define and investigate some basic properties of generalized grand\\nWiener amalgam space $W( L^{p),\\\\theta_1}(\\\\mathbb R^{n})),\\nL^{q),\\\\theta_2}(\\\\mathbb R^{n})),$ where generalized grand Lebesgue spaces\\n$L_{a}^{p)}(\\\\mathbb R^{n})$ and $L_{b}^{q)}(\\\\mathbb R^{n}),$ are local and\\nglobal components, respectively. Next we study embeddings for these spaces,\\nalso we give some more properties of these spaces. At the end of this work, we\\ndiscuss boundedness and unboundedness of the Hardy-Littlewood maximal operator\\nbetween some generalized grand Wiener amalgam spaces.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"8 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.02406\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.02406","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}