SMOOTHING ESTIMATES OF THE RADIAL SCHRODINGER PROPAGATOR IN DIMENSIONS n >= 2

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	SMOOTHING ESTIMATES OF THE RADIAL SCHRODINGER PROPAGATOR IN DIMENSIONS n >= 2
	Li Dong 1; Zhang Xiaoyi 1,2
	2010-11-01
发表期刊	ACTA MATHEMATICA SCIENTIA
ISSN	0252-9602
卷号	30 期号:6 页码:2103-2109
摘要	The usual Kato smoothing estimate for the Schrodinger propagator in 1D takes the form parallel to vertical bar partial derivative(x)vertical bar(1/2)e(it partial derivative xx)u(0)parallel to L(x)(infinity)L(t)(2) less than or similar to parallel to u(0)parallel to L(x)(2). In dimensions n >= 2 the smoothing estimate involves certain localization to cubes in space. In this paper we focus on radial functions and obtain Kato-type sharp smoothing estimates which can be viewed as natural generalizations of the 1D Kato smoothing. These estimates are global in the sense that they do not need localization in space. We also present an interesting counterexample which shows that even though the time-global inhomogeneous Kato smoothing holds true, the corresponding time-local inhomogeneous smoothing estimate cannot hold in general.
关键词	Schrodinger equation smoothing estimate
语种	英语
资助项目	NSF[0908032] ; University of Iowa ; Alfred P. Sloan fellowship
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000284793000019
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9777
专题	中国科学院数学与系统科学研究院
通讯作者	Li Dong
作者单位	1.Univ Iowa, Dept Math, Iowa City, IA 52242 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li Dong,Zhang Xiaoyi. SMOOTHING ESTIMATES OF THE RADIAL SCHRODINGER PROPAGATOR IN DIMENSIONS n >= 2[J]. ACTA MATHEMATICA SCIENTIA,2010,30(6):2103-2109.
APA	Li Dong,&Zhang Xiaoyi.(2010).SMOOTHING ESTIMATES OF THE RADIAL SCHRODINGER PROPAGATOR IN DIMENSIONS n >= 2.ACTA MATHEMATICA SCIENTIA,30(6),2103-2109.
MLA	Li Dong,et al."SMOOTHING ESTIMATES OF THE RADIAL SCHRODINGER PROPAGATOR IN DIMENSIONS n >= 2".ACTA MATHEMATICA SCIENTIA 30.6(2010):2103-2109.