{"title":"分数维中具有对数权值的亚当斯型不等式和极值的存在性","authors":"Rou Jiang , Wenyan Xu , Caifeng Zhang , Maochun Zhu","doi":"10.1016/j.bulsci.2025.103586","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we proved a sharp Adams-type inequality with logarithmic weights <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> or <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>, <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> in the fractional dimensions. Furthermore, we show the existence of extremals for this kind of inequalities.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103586"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adams-type inequalities with logarithmic weights in fractional dimensions and the existence of extremals\",\"authors\":\"Rou Jiang , Wenyan Xu , Caifeng Zhang , Maochun Zhu\",\"doi\":\"10.1016/j.bulsci.2025.103586\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we proved a sharp Adams-type inequality with logarithmic weights <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> or <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo></mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>, <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> in the fractional dimensions. Furthermore, we show the existence of extremals for this kind of inequalities.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"200 \",\"pages\":\"Article 103586\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449725000120\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725000120","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Adams-type inequalities with logarithmic weights in fractional dimensions and the existence of extremals
In this paper, we proved a sharp Adams-type inequality with logarithmic weights or , in the fractional dimensions. Furthermore, we show the existence of extremals for this kind of inequalities.