{"title":"On a generalized Möbius invariant function space","authors":"Xiaojing Zhou","doi":"10.1016/j.jmaa.2024.128979","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, <span><math><msubsup><mrow><mi>B</mi></mrow><mrow><mi>α</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>, <span><math><msubsup><mrow><mtext>BMOA</mtext></mrow><mrow><mi>p</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span>, and <span><math><mi>F</mi><mo>(</mo><mi>p</mi><mo>,</mo><mi>p</mi><mi>α</mi><mo>−</mo><mn>2</mn><mo>,</mo><mi>s</mi><mo>)</mo></math></span> as particular cases. We study several basic properties of such new spaces and also characterize these spaces via Carleson-type measures. As for some applications, we study the corresponding little-o spaces, as well as establish several embedding relations of these new spaces with Bloch-type spaces. Our result generalizes an early work of Zhu in 2007.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009016","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
In this paper, we introduce a new class of generalized Möbius function space of analytic functions in the unit disk, that contains , , , and as particular cases. We study several basic properties of such new spaces and also characterize these spaces via Carleson-type measures. As for some applications, we study the corresponding little-o spaces, as well as establish several embedding relations of these new spaces with Bloch-type spaces. Our result generalizes an early work of Zhu in 2007.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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