{"title":"点式稀疏支配导论","authors":"Rodrigo Duarte","doi":"10.1016/j.exmath.2024.125605","DOIUrl":null,"url":null,"abstract":"<div><p>The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it allows for a unified approach to proving weighted norm inequalities for a large variety of operators. In this work, we will introduce the basic ideas of dyadic Harmonic Analysis, which we use to build up to the main result we discuss on pointwise sparse domination, which is the Lerner–Ombrosi theorem. We also give applications of this theorem to some families of operators, mainly relating to singular integral operators. The text has been structured so as to motivate the introduction of new ideas through the lens of solving specific problems in Harmonic Analysis.</p></div>","PeriodicalId":50458,"journal":{"name":"Expositiones Mathematicae","volume":"42 6","pages":"Article 125605"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0723086924000720/pdfft?md5=45dd60e1ad35b7a191fa8e59cc8e5e5d&pid=1-s2.0-S0723086924000720-main.pdf","citationCount":"0","resultStr":"{\"title\":\"An introduction to pointwise sparse domination\",\"authors\":\"Rodrigo Duarte\",\"doi\":\"10.1016/j.exmath.2024.125605\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it allows for a unified approach to proving weighted norm inequalities for a large variety of operators. In this work, we will introduce the basic ideas of dyadic Harmonic Analysis, which we use to build up to the main result we discuss on pointwise sparse domination, which is the Lerner–Ombrosi theorem. We also give applications of this theorem to some families of operators, mainly relating to singular integral operators. The text has been structured so as to motivate the introduction of new ideas through the lens of solving specific problems in Harmonic Analysis.</p></div>\",\"PeriodicalId\":50458,\"journal\":{\"name\":\"Expositiones Mathematicae\",\"volume\":\"42 6\",\"pages\":\"Article 125605\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0723086924000720/pdfft?md5=45dd60e1ad35b7a191fa8e59cc8e5e5d&pid=1-s2.0-S0723086924000720-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Expositiones Mathematicae\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0723086924000720\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Expositiones Mathematicae","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0723086924000720","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The goal of this expository paper is to give a self-contained introduction to sparse domination. This is a method relying on techniques from dyadic Harmonic Analysis which has received a lot of attention in recent years. Essentially, it allows for a unified approach to proving weighted norm inequalities for a large variety of operators. In this work, we will introduce the basic ideas of dyadic Harmonic Analysis, which we use to build up to the main result we discuss on pointwise sparse domination, which is the Lerner–Ombrosi theorem. We also give applications of this theorem to some families of operators, mainly relating to singular integral operators. The text has been structured so as to motivate the introduction of new ideas through the lens of solving specific problems in Harmonic Analysis.
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Our aim is to publish papers of interest to a wide mathematical audience. Our main interest is in expository articles that make high-level research results more widely accessible. In general, material submitted should be at least at the graduate level.Main articles must be written in such a way that a graduate-level research student interested in the topic of the paper can read them profitably. When the topic is quite specialized, or the main focus is a narrow research result, the paper is probably not appropriate for this journal. Most original research articles are not suitable for this journal, unless they have particularly broad appeal.Mathematical notes can be more focused than main articles. These should not simply be short research articles, but should address a mathematical question with reasonably broad appeal. Elementary solutions of elementary problems are typically not appropriate. Neither are overly technical papers, which should best be submitted to a specialized research journal.Clarity of exposition, accuracy of details and the relevance and interest of the subject matter will be the decisive factors in our acceptance of an article for publication. Submitted papers are subject to a quick overview before entering into a more detailed review process. All published papers have been refereed.
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