{"title":"一个Carleson型测度和一个Möbius不变函数空间族","authors":"Guanlong Bao , Fangqin Ye","doi":"10.1016/j.indag.2023.06.005","DOIUrl":null,"url":null,"abstract":"<div><p>For <span><math><mrow><mn>0</mn><mo><</mo><mi>s</mi><mo><</mo><mn>1</mn></mrow></math></span>, let <span><math><mrow><mo>{</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></math></span><span> be a sequence in the open unit disk such that </span><span><math><mrow><msub><mrow><mo>∑</mo></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><msub><mrow><mi>δ</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></mrow></math></span> is an <em>s</em>-Carleson measure. In this paper, we consider the connections between this <em>s</em>-Carleson measure and the theory of Möbius invariant <em>F(p, p-2, s)</em> spaces by the Volterra type operator, the reciprocal of a Blaschke product, and second order complex differential equations having a prescribed zero sequence.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Carleson type measure and a family of Möbius invariant function spaces\",\"authors\":\"Guanlong Bao , Fangqin Ye\",\"doi\":\"10.1016/j.indag.2023.06.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For <span><math><mrow><mn>0</mn><mo><</mo><mi>s</mi><mo><</mo><mn>1</mn></mrow></math></span>, let <span><math><mrow><mo>{</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>}</mo></mrow></math></span><span> be a sequence in the open unit disk such that </span><span><math><mrow><msub><mrow><mo>∑</mo></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mrow><mo>|</mo><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><msub><mrow><mi>δ</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></mrow></math></span> is an <em>s</em>-Carleson measure. In this paper, we consider the connections between this <em>s</em>-Carleson measure and the theory of Möbius invariant <em>F(p, p-2, s)</em> spaces by the Volterra type operator, the reciprocal of a Blaschke product, and second order complex differential equations having a prescribed zero sequence.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-07-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0019357723000599\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357723000599","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Carleson type measure and a family of Möbius invariant function spaces
For , let be a sequence in the open unit disk such that is an s-Carleson measure. In this paper, we consider the connections between this s-Carleson measure and the theory of Möbius invariant F(p, p-2, s) spaces by the Volterra type operator, the reciprocal of a Blaschke product, and second order complex differential equations having a prescribed zero sequence.
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