{"title":"Conformal images of Carleson curves","authors":"C. Bishop","doi":"10.1090/bproc/69","DOIUrl":null,"url":null,"abstract":"<p>We show that if <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\n <mml:semantics>\n <mml:mi>γ<!-- γ --></mml:mi>\n <mml:annotation encoding=\"application/x-tex\">\\gamma</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is a curve in the unit disk, then arclength on <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\n <mml:semantics>\n <mml:mi>γ<!-- γ --></mml:mi>\n <mml:annotation encoding=\"application/x-tex\">\\gamma</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is a Carleson measure iff the image of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"gamma\">\n <mml:semantics>\n <mml:mi>γ<!-- γ --></mml:mi>\n <mml:annotation encoding=\"application/x-tex\">\\gamma</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> has finite length under every conformal map of the disk onto a bounded domain with a rectifiable boundary.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"133 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society, Series B","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/bproc/69","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that if γ\gamma is a curve in the unit disk, then arclength on γ\gamma is a Carleson measure iff the image of γ\gamma has finite length under every conformal map of the disk onto a bounded domain with a rectifiable boundary.
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