Andrea Pinamonti , Gareth Speight , Scott Zimmerman
{"title":"海森堡群中水平曲线的高阶惠特尼扩展和卢辛近似","authors":"Andrea Pinamonti , Gareth Speight , Scott Zimmerman","doi":"10.1016/j.matpur.2024.06.005","DOIUrl":null,"url":null,"abstract":"<div><p>In the setting of horizontal curves in the Heisenberg group, we prove a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> finiteness principle, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> Lusin approximation result, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Whitney extension result, and a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span>, and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> in the Heisenberg group.</p></div>","PeriodicalId":51071,"journal":{"name":"Journal de Mathematiques Pures et Appliquees","volume":"188 ","pages":"Pages 320-344"},"PeriodicalIF":2.1000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021782424000801/pdfft?md5=f47e1c136eb6a58b1e26a2db9f54d4d9&pid=1-s2.0-S0021782424000801-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group\",\"authors\":\"Andrea Pinamonti , Gareth Speight , Scott Zimmerman\",\"doi\":\"10.1016/j.matpur.2024.06.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the setting of horizontal curves in the Heisenberg group, we prove a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> finiteness principle, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span> Lusin approximation result, a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Whitney extension result, and a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>m</mi><mo>,</mo><mi>ω</mi></mrow></msup></math></span>, and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span> in the Heisenberg group.</p></div>\",\"PeriodicalId\":51071,\"journal\":{\"name\":\"Journal de Mathematiques Pures et Appliquees\",\"volume\":\"188 \",\"pages\":\"Pages 320-344\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-06-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000801/pdfft?md5=f47e1c136eb6a58b1e26a2db9f54d4d9&pid=1-s2.0-S0021782424000801-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de Mathematiques Pures et Appliquees\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021782424000801\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de Mathematiques Pures et Appliquees","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021782424000801","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Higher order Whitney extension and Lusin approximation for horizontal curves in the Heisenberg group
In the setting of horizontal curves in the Heisenberg group, we prove a finiteness principle, a Lusin approximation result, a Whitney extension result, and a Lusin approximation result. Combined with previous work, this completes the study of Whitney extension and Lusin approximation for horizontal curves of class , , and in the Heisenberg group.
期刊介绍:
Published from 1836 by the leading French mathematicians, the Journal des Mathématiques Pures et Appliquées is the second oldest international mathematical journal in the world. It was founded by Joseph Liouville and published continuously by leading French Mathematicians - among the latest: Jean Leray, Jacques-Louis Lions, Paul Malliavin and presently Pierre-Louis Lions.