Interpolation of derivatives and ultradifferentiable regularity

IF 0.8 3区数学 Q2 MATHEMATICS Mathematische Nachrichten Pub Date : 2024-12-18 DOI:10.1002/mana.202300567

Armin Rainer, Gerhard Schindl

{"title":"Interpolation of derivatives and ultradifferentiable regularity","authors":"Armin Rainer, Gerhard Schindl","doi":"10.1002/mana.202300567","DOIUrl":null,"url":null,"abstract":"Interpolation inequalities for <math>\n <semantics>\n <msup>\n <mi>C</mi>\n <mi>m</mi>\n </msup>\n <annotation>$C^m$</annotation>\n </semantics></math> functions allow to bound derivatives of intermediate order <math>\n <semantics>\n <mrow>\n <mn>0</mn>\n <mo><</mo>\n <mi>j</mi>\n <mo><</mo>\n <mi>m</mi>\n </mrow>\n <annotation>$0 < j<m$</annotation>\n </semantics></math> by bounds for the derivatives of order 0 and <math>\n <semantics>\n <mi>m</mi>\n <annotation>$m$</annotation>\n </semantics></math>. We review various interpolation inequalities for <math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mi>p</mi>\n </msup>\n <annotation>$L^p$</annotation>\n </semantics></math>-norms (<math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>≤</mo>\n <mi>p</mi>\n <mo>≤</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$1 \\le p \\le \\infty$</annotation>\n </semantics></math>) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"298 2","pages":"617-635"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202300567","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300567","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

Abstract

Interpolation inequalities for $C^{m}$ functions allow to bound derivatives of intermediate order $0 < j < m$ by bounds for the derivatives of order 0 and $m$ . We review various interpolation inequalities for $L^{p}$ -norms ( $1 \leq p \leq \infty$ ) in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.

Abstract Image

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

导数插值与超可微正则性

C m $C^m$函数的插值不等式允许中阶导数为0 ＆lt；J ＆ t；M $0 < j<m$通过0阶导数和M $m$的界。我们回顾了任意有限维的L p $L^p$ -范数（1≤p≤∞$1 \le p \le \infty$）的各种插值不等式。它们使我们能够以一种综合的方式通过空间估计来研究超可微正则性，力求对权重的最小假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index

期刊最新文献

Issue Information Contents Solvability of invariant systems of differential equations on H 2 $\mathbb {H}^2$ and beyond Issue Information Contents