{"title":"Calderón-Zygmund分数阶p-拉普拉斯算子的估计","authors":"Lars Diening, Simon Nowak","doi":"10.1007/s40818-025-00196-1","DOIUrl":null,"url":null,"abstract":"<div><p>We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional <i>p</i>-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions. This approach is new already in the linear setting and enables us to deduce sharp regularity results also in borderline cases.</p></div>","PeriodicalId":36382,"journal":{"name":"Annals of Pde","volume":"11 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2025-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40818-025-00196-1.pdf","citationCount":"0","resultStr":"{\"title\":\"Calderón–Zygmund Estimates for the Fractional p-Laplacian\",\"authors\":\"Lars Diening, Simon Nowak\",\"doi\":\"10.1007/s40818-025-00196-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional <i>p</i>-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions. This approach is new already in the linear setting and enables us to deduce sharp regularity results also in borderline cases.</p></div>\",\"PeriodicalId\":36382,\"journal\":{\"name\":\"Annals of Pde\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2025-01-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s40818-025-00196-1.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pde\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40818-025-00196-1\",\"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":"Annals of Pde","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40818-025-00196-1","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Calderón–Zygmund Estimates for the Fractional p-Laplacian
We prove fine higher regularity results of Calderón-Zygmund-type for equations involving nonlocal operators modelled on the fractional p-Laplacian with possibly discontinuous coefficients of VMO-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions. This approach is new already in the linear setting and enables us to deduce sharp regularity results also in borderline cases.
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