{"title":"功能空间中的构建块","authors":"H. Triebel","doi":"10.1007/s10476-023-0236-0","DOIUrl":null,"url":null,"abstract":"<div><p>The spaces <i>A</i><span>\n <sup><i>s</i></sup><sub><i>p,q</i></sub>\n \n </span>(ℝ<sup><i>n</i></sup>)with <i>A</i> ∈ {<i>B, F</i>}, <i>s</i> ∈ ℝ and 0 <<i>p,q</i> ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces <i>A</i><span>\n <sup><i>s</i></sup><sub><i>p,q</i></sub>\n \n </span>(ℝ<sup><i>n</i></sup>) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions <i>f</i> ∈ <i>S</i>′(ℝ<sup><i>n</i></sup>).</p></div>","PeriodicalId":55518,"journal":{"name":"Analysis Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Building Blocks in Function Spaces\",\"authors\":\"H. Triebel\",\"doi\":\"10.1007/s10476-023-0236-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The spaces <i>A</i><span>\\n <sup><i>s</i></sup><sub><i>p,q</i></sub>\\n \\n </span>(ℝ<sup><i>n</i></sup>)with <i>A</i> ∈ {<i>B, F</i>}, <i>s</i> ∈ ℝ and 0 <<i>p,q</i> ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces <i>A</i><span>\\n <sup><i>s</i></sup><sub><i>p,q</i></sub>\\n \\n </span>(ℝ<sup><i>n</i></sup>) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions <i>f</i> ∈ <i>S</i>′(ℝ<sup><i>n</i></sup>).</p></div>\",\"PeriodicalId\":55518,\"journal\":{\"name\":\"Analysis Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0236-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis Mathematica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0236-0","RegionNum":3,"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
摘要
当A∈{B, F}， s∈∈，且0 <p,q≤∞时，空间A sp,q(∈n)通常用傅里叶解析分解的形式引入。以原子和小波为基础的相关表征，如今已相当彻底地为人所知。夸克使原子原子化，形成有建设性的构件。本研究的主要目的是将夸克分解提升到与空间A sp,q (v n)在原子或小波方面的相关表示相同的水平，最终达到缓和分布f∈S ' (v n)的普遍框架表示。
The spaces Asp,q(ℝn)with A ∈ {B, F}, s ∈ ℝ and 0 <p,q ≤ ∞ are usually introduced in terms of Fourier-analytical decompositions. Related characterizations based on atoms and wavelets are known nowadays in a rather final way. Quarks atomize the atoms into constructive building blocks. It is the main aim of this survey to raise quarkonial decompositions to the same level as related representations of the spaces Asp,q(ℝn) in terms of atoms or wavelets culminating finally in universal frame representations of tempered distributions f ∈ S′(ℝn).
期刊介绍：
Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx).
The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx).
The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.
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