{"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":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae-New Series","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0019357723000599","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍:
Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.