南方科技大学知识苑(SUSTech KC): Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures

题名	Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures
作者	Liu, Bochen1,2
通讯作者	Liu, Bochen
发表日期	2024
DOI	10.4171/RMI/1472
发表期刊	REVISTA MATEMATICA IBEROAMERICANA 影响因子和分区
ISSN	0213-2230
卷号	40 期号:3
摘要	Suppose that mu and v are compactly supported Radon measures on R d , V E G(d, n) is an n -dimensional subspace, and let n V : R d -* V denote the orthogonal projection. In this paper, we study the mixed -norm R II n y mu II q L p ( G( d, n)) dv(y) , where Z n y mu (V ) := y C V ? mu dde d - n = n V mu (n V y), assuming mu has continuous density. When n = d - 1 and p = q , our result significantly improves a previous result of Orponen on radial projections. We also discuss about consequences including jump discontinuities in the range of p , and m -planes determined by a set of given Hausdorff dimension. In the proof, we run analytic interpolation not only on p and q , but also on dimensions of measures. This is partially inspired by previous work of Greenleaf and Iosevich on Falconer -type problems. We also introduce a new quantity called s -amplitude, that is crucial for our interpolation and gives an alternative definition of Hausdorff dimension.
关键词	orthogonal projection radial projection analytic interpolation
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	第一 ; 通讯
资助项目	National Natural Science Foundation of China[12131011]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:001226304700012
出版者	EUROPEAN MATHEMATICAL SOC-EMS
ESI学科分类	MATHEMATICS
来源库	Web of Science
引用统计
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/788348
专题	理学院_数学系南方科技大学
作者单位	1.Southern Univ Sci & Technol, Dept Math, 1088 Xueyuan Ave, Shenzhen 518055, Peoples R China 2.Southern Univ Sci & Technol, Int Ctr Math, 1088 Xueyuan Ave, Shenzhen 518055, Peoples R China
第一作者单位	数学系; 南方科技大学
通讯作者单位	数学系; 南方科技大学
第一作者的第一单位	数学系
推荐引用方式 GB/T 7714	Liu, Bochen. Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures[J]. REVISTA MATEMATICA IBEROAMERICANA,2024,40(3).
APA	Liu, Bochen.(2024).Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures.REVISTA MATEMATICA IBEROAMERICANA,40(3).
MLA	Liu, Bochen."Mixed-norm of orthogonal projections and analytic interpolation on dimensions of measures".REVISTA MATEMATICA IBEROAMERICANA 40.3(2024).