Marcinkiewicz 积分在加权Hardy 空间和加权Herz 型Hardy 空间上的弱型估计

数学物理学报 ›› 2012, Vol. 32 ›› Issue (5): 840-850.

Marcinkiewicz 积分在加权Hardy 空间和加权Herz 型Hardy 空间上的弱型估计

王华

浙江大学数学系杭州 310027

收稿日期:2011-03-18 修回日期:2012-06-14 出版日期:2012-10-25 发布日期:2012-10-25
基金资助:
国家自然科学基金(10871173, 10931001)资助

Weak Type Estimates of Marcinkiewicz Integrals on the Weighted Hardy and Herz-type Hardy Spaces

WANG Hua

Department of Mathematics, Zhejiang University, Hangzhou 310027

Received:2011-03-18 Revised:2012-06-14 Online:2012-10-25 Published:2012-10-25
Supported by:
国家自然科学基金(10871173, 10931001)资助

摘要/Abstract

摘要：

Marcinkiewicz 积分本质上是一个Littlewood-Paley g-函数, 它在调和分析的研究中起着很重要的作用. 该文将利用加权Hardy 空间和齐次加权 Herz 型Hardy 空间的原子分解理论来证明Marcinkiewicz 积分在这些空间上的加权弱型估计.

关键词: Marcinkiewicz 积分, 加权Hardy 空间, 加权Herz 型Hardy 空间, A_p 权, 原子分解

Abstract:

The Marcinkiewicz integral is essentially a Littlewood-Paley g-function, which plays an important role in harmonic analysis. In this article, by using the atomic decomposition theory of weighted Hardy spaces and homogeneous weighted Herz-type Hardy spaces, we obtain some weighted weak type estimates for Marcinkiewicz integrals on these spaces.

Key words: Marcinkiewicz integrals, Weighted Hardy spaces, Weighted Herz-type Hardy spaces, A_p weights, Atomic decomposition

中图分类号:

42B25

王华. Marcinkiewicz 积分在加权Hardy 空间和加权Herz 型Hardy 空间上的弱型估计[J]. 数学物理学报, 2012, 32(5): 840-850.

WANG Hua. Weak Type Estimates of Marcinkiewicz Integrals on the Weighted Hardy and Herz-type Hardy Spaces[J]. Acta mathematica scientia,Series A, 2012, 32(5): 840-850.

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