加幂权Hardy算子的(L1, Lq)-有界性的充要条件

doi:10.7523/j.issn.2095-6134.2013.06.002

中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (6): 724-727.DOI: 10.7523/j.issn.2095-6134.2013.06.002

加幂权Hardy算子的(L¹, L^q)-有界性的充要条件

聂旭东¹, 王士模², 燕敦验¹

1. 中国科学院大学数学科学学院, 北京 100049;
2. 黑龙江大学数学科学学院, 哈尔滨 150080

收稿日期:2013-03-01 修回日期:2013-04-24 发布日期:2013-11-15
通讯作者: 燕敦验
基金资助:
Supported by the National Nature Science Foundation of China(10771221,11271162) and Foundation of University of Chinese Academy of Sciences(Y05102AN00)

Sufficient and necessary conditions of (L¹, L^q)-boundedness for Hardy operator with power weight

NIE Xu-Dong¹, WANG Shi-Mo², YAN Dun-Yan¹

1 School of Mathematics Science, University of Chinese Academy of Sciences, Beijing 100049, China;
2 School of Mathematics Science, Heilongjiang University, Harbin 150080, China

Received:2013-03-01 Revised:2013-04-24 Published:2013-11-15

摘要/Abstract

摘要：

分别得到使得n维空间上 Hardy算子H_n及其对偶算子H_n^*,从L_|x|α¹( R ⁿ)到L_|x|β^q(Rⁿ) (1≤q<∞) 有界的关于α和β所需满足的充分必要条件.

关键词: Hardy算子, 对偶算子, 幂权, 端点估计

Abstract:

We characterize the sufficient and necessary conditions with respect to α and β which make the Hardy operator H_n and the Hardy operator's conjugate operator H_n^* be bounded from L_|x|α¹(Rⁿ) to L_|x|β^q( R ⁿ) with 1≤q<∞ in n-dimensional Euclidean spaces, respectively.

Key words: Hardy operator, conjugate operator, power weight, endpoint estimates

中图分类号:

O174.1

聂旭东, 王士模, 燕敦验. 加幂权Hardy算子的(L¹, L^q)-有界性的充要条件[J]. 中国科学院大学学报, 2013, 30(6): 724-727.

NIE Xu-Dong, WANG Shi-Mo, YAN Dun-Yan. Sufficient and necessary conditions of (L¹, L^q)-boundedness for Hardy operator with power weight[J]. , 2013, 30(6): 724-727.

加幂权Hardy算子的(L¹, L^q)-有界性的充要条件

Sufficient and necessary conditions of (L¹, L^q)-boundedness for Hardy operator with power weight

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