利用稀疏主宰法表征正向、消失和反向伯格曼-卡列松量纲

Pub Date : 2024-06-28 DOI:10.1007/s11785-024-01565-7
Hamzeh Keshavarzi
{"title":"利用稀疏主宰法表征正向、消失和反向伯格曼-卡列松量纲","authors":"Hamzeh Keshavarzi","doi":"10.1007/s11785-024-01565-7","DOIUrl":null,"url":null,"abstract":"<p>In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. In the case of forward and vanishing Bergman Carleson measures, our results extend the results of [J Funct Anal 280(6):26, 2021] from <span>\\(1\\leqslant p\\leqslant q&lt; 2p\\)</span> to all <span>\\(0&lt;p\\leqslant q&lt;\\infty \\)</span>. In a more general case, we characterize the positive Borel measures <span>\\(\\mu \\)</span> on <span>\\(\\mathbb {B}\\)</span> so that the radial differentiation operator <span>\\(R^{k}:A_\\omega ^p(\\mathbb {B})\\rightarrow L^q(\\mathbb {B},\\mu )\\)</span> is bounded and compact. Although we consider the weighted Bergman spaces induced by two-side doubling weights, the results are new even on classical weighted Bergman spaces.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Characterization of Forward, Vanishing, and Reverse Bergman Carleson Measures using Sparse Domination\",\"authors\":\"Hamzeh Keshavarzi\",\"doi\":\"10.1007/s11785-024-01565-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. In the case of forward and vanishing Bergman Carleson measures, our results extend the results of [J Funct Anal 280(6):26, 2021] from <span>\\\\(1\\\\leqslant p\\\\leqslant q&lt; 2p\\\\)</span> to all <span>\\\\(0&lt;p\\\\leqslant q&lt;\\\\infty \\\\)</span>. In a more general case, we characterize the positive Borel measures <span>\\\\(\\\\mu \\\\)</span> on <span>\\\\(\\\\mathbb {B}\\\\)</span> so that the radial differentiation operator <span>\\\\(R^{k}:A_\\\\omega ^p(\\\\mathbb {B})\\\\rightarrow L^q(\\\\mathbb {B},\\\\mu )\\\\)</span> is bounded and compact. Although we consider the weighted Bergman spaces induced by two-side doubling weights, the results are new even on classical weighted Bergman spaces.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-024-01565-7\",\"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://doi.org/10.1007/s11785-024-01565-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们利用谐波分析中一种叫做稀疏支配的新技术,描述了包括正向、消失和反向伯格曼-卡列森量在内的正伯格曼量的特征。在正向和消失的伯格曼-卡莱森度量的情况下,我们的结果扩展了[J Funct Anal 280(6):26, 2021]的结果,从\(1\leqslant p\leqslant q< 2p\)到所有\(0<p\leqslant q<\infty \)。在更一般的情况下,我们描述了 \(\mathbb {B}\)上的正(Borel)度量 \(\mathbb {B}\),这样径向微分算子 \(R^{k}:A_\omega ^p(\mathbb {B})\rightarrow L^q(\mathbb {B},\mu)\)是有界的、紧凑的。虽然我们考虑的是由两边加倍权重诱导的加权伯格曼空间,但即使在经典加权伯格曼空间上,这些结果也是新的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
Characterization of Forward, Vanishing, and Reverse Bergman Carleson Measures using Sparse Domination

In this paper, using a new technique from harmonic analysis called sparse domination, we characterize the positive Borel measures including forward, vanishing, and reverse Bergman Carleson measures. In the case of forward and vanishing Bergman Carleson measures, our results extend the results of [J Funct Anal 280(6):26, 2021] from \(1\leqslant p\leqslant q< 2p\) to all \(0<p\leqslant q<\infty \). In a more general case, we characterize the positive Borel measures \(\mu \) on \(\mathbb {B}\) so that the radial differentiation operator \(R^{k}:A_\omega ^p(\mathbb {B})\rightarrow L^q(\mathbb {B},\mu )\) is bounded and compact. Although we consider the weighted Bergman spaces induced by two-side doubling weights, the results are new even on classical weighted Bergman spaces.

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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信