{"title":"简单连通恒定曲率空间上完全大地拉顿变换的端点估计:统一方法","authors":"Aniruddha Deshmukh, Ashisha Kumar","doi":"arxiv-2408.13541","DOIUrl":null,"url":null,"abstract":"In this article, we give a unified proof of the end-point estimates of the\ntotally-geodesic $k$-plane transform of radial functions on spaces of constant\ncurvature. The problem of getting end-point estimates is not new and some\nresults are available in literature. However, these results were obtained\nindependently without much focus on the similarities between underlying\ngeometries. We give a unified proof for the end-point estimates on spaces of\nconstant curvature by making use of geometric ideas common to the spaces of\nconstant curvature, and obtaining a unified formula for the $k$-plane transform\nof radial functions. We also give some inequalities for certain special\nfunctions as an application to one of our lemmata.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"25 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach\",\"authors\":\"Aniruddha Deshmukh, Ashisha Kumar\",\"doi\":\"arxiv-2408.13541\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we give a unified proof of the end-point estimates of the\\ntotally-geodesic $k$-plane transform of radial functions on spaces of constant\\ncurvature. The problem of getting end-point estimates is not new and some\\nresults are available in literature. However, these results were obtained\\nindependently without much focus on the similarities between underlying\\ngeometries. We give a unified proof for the end-point estimates on spaces of\\nconstant curvature by making use of geometric ideas common to the spaces of\\nconstant curvature, and obtaining a unified formula for the $k$-plane transform\\nof radial functions. We also give some inequalities for certain special\\nfunctions as an application to one of our lemmata.\",\"PeriodicalId\":501036,\"journal\":{\"name\":\"arXiv - MATH - Functional Analysis\",\"volume\":\"25 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.13541\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13541","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
End-point estimates of the totally-geodesic Radon transform on simply connected spaces of constant curvature: A Unified Approach
In this article, we give a unified proof of the end-point estimates of the
totally-geodesic $k$-plane transform of radial functions on spaces of constant
curvature. The problem of getting end-point estimates is not new and some
results are available in literature. However, these results were obtained
independently without much focus on the similarities between underlying
geometries. We give a unified proof for the end-point estimates on spaces of
constant curvature by making use of geometric ideas common to the spaces of
constant curvature, and obtaining a unified formula for the $k$-plane transform
of radial functions. We also give some inequalities for certain special
functions as an application to one of our lemmata.