球上Bergman空间上复合算子的紧二重差

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2019-12-01 DOI:10.2748/tmj/1576724796

B. Choe, H. Koo, Jongho Yang

{"title":"球上Bergman空间上复合算子的紧二重差","authors":"B. Choe, H. Koo, Jongho Yang","doi":"10.2748/tmj/1576724796","DOIUrl":null,"url":null,"abstract":"Choe et. al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.","PeriodicalId":54427,"journal":{"name":"Tohoku Mathematical Journal","volume":"71 1","pages":"609-637"},"PeriodicalIF":0.4000,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Compact double differences of composition operators on the Bergman spaces over the ball\",\"authors\":\"B. Choe, H. Koo, Jongho Yang\",\"doi\":\"10.2748/tmj/1576724796\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Choe et. al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.\",\"PeriodicalId\":54427,\"journal\":{\"name\":\"Tohoku Mathematical Journal\",\"volume\":\"71 1\",\"pages\":\"609-637\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2019-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tohoku Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2748/tmj/1576724796\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tohoku Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2748/tmj/1576724796","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

Choe等人最近刻画了由四个复合算子作用在复平面圆盘上的标准加权Bergman空间上形成的紧致二重差。在本文中，我们将这一结果推广到球的设置中。我们的特征是在诱导映射的适当限制下获得的，这在圆盘的情况下是自动满足的。我们展示了具体的例子，这是第一次，即使是单成分算子，这表明这种限制在球的情况下是必不可少的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Compact double differences of composition operators on the Bergman spaces over the ball

Choe et. al. have recently characterized compact double differences formed by four composition operators acting on the standard weighted Bergman spaces over the disk of the complex plane. In this paper, we extend such a result to the ball setting. Our characterization is obtained under a suitable restriction on inducing maps, which is automatically satisfied in the case of the disk. We exhibit concrete examples, for the first time even for single composition operators, which shows that such a restriction is essential in the case of the ball.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊