(Lr,Ls) 1 r−1 s = 2 n线外球面的解析估计

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2019-05-12 DOI:10.1142/S1664360719500036

Tianyi Ren

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引用次数: 1

摘要

我们将球面上的解析估计扩展到线外指数[公式:见文本]。由于指数上的条件[公式:见文本]是一致界的必要条件，因此不能期望这条线上的估计仍然是一致的。我们证明的基本要素是一个[公式:见文]对算子[公式:见文]的范数估计，它投射到次次的球面谐波空间[公式:见文]。为了显示这个估计，我们采用了布尔甘(Bourgain)首先引入的插值技术[J]。布尔甘，函数极值的估计，中国科学院学报。巴黎爵士。[j].数学。301(10)(1985)499-502。我们其余的证明与Huang-Sogge [S。黄和c.d. Sogge，关于常曲率单连通流形的解析估计[公式:见文本]，J. Funct。[j].中国科学院学报。267(12)(2014)4635-4666。

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(Lr,Ls) Resolvent estimate for the sphere off the line 1 r −1 s = 2 n

We extend the resolvent estimate on the sphere to exponents off the line [Formula: see text]. Since the condition [Formula: see text] on the exponents is necessary for a uniform bound, one cannot expect estimates off this line to be uniform still. The essential ingredient in our proof is an [Formula: see text] norm estimate on the operator [Formula: see text] that projects onto the space of spherical harmonics of degree [Formula: see text]. In showing this estimate, we apply an interpolation technique first introduced by Bourgain [J. Bourgain, Estimations de certaines fonctions maximales, C. R. Acad. Sci. Paris Sér. I Math. 301(10) (1985) 499–502.]. The rest of our proof parallels that in Huang–Sogge [S. Huang and C. D. Sogge, Concerning [Formula: see text] resolvent estimates for simply connected manifolds of constant curvature, J. Funct. Anal. 267(12) (2014) 4635–4666].

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.