Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）

齐春燕; 张惠; 李宝德

doi:10.13568/j.cnki.651094.2016.03.007

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Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）

数理科学 | 更新时间：2026-01-21

- Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）
- Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）
- 新疆大学学报（自然科学版中英文） 2016年33卷第3期页码：287-295
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  supported by the National Natural Science Foundation of China(11461065);Scientific Research Projects in Colleges and Universities in Xinjiang Uyghur Autonomous Region(XJEDU2014S001)
- DOI：10.13568/j.cnki.651094.2016.03.007
  中图分类号： O177
- 纸质出版：2016
- 稿件说明：
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[1]齐春燕,张惠,李宝德.Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）[J].新疆大学学报(自然科学版),2016,33(03):287-295.
[1]齐春燕,张惠,李宝德.Littlewood-Paley函数在各向异性Musielak-Orlicz型弱Hardy空间上的有界性（英文）[J].新疆大学学报(自然科学版),2016,33(03):287-295. DOI： 10.13568/j.cnki.651094.2016.03.007.

DOI：10.13568/j.cnki.651094.2016.03.007.

摘要

设A是一个扩张矩阵

p∈(0

1]及?:Rn×[0

∞)→[0

∞)是一个各向异性p-增长函数.本文通过主极大函数定义了各向异性Musielak-Orlicz型弱Hardy空间H?

∞A(Rn)

并用此空间上的原子分解证明了各向异性LittlewoodPaley Lusin-area函数

各向异性g-函数及各向异性g*λ-函数从H?

∞A(Rn)到弱Musielak-Orlicz-型空间上的有界性.我们指出在g*λ-函数关于空间H?

∞A(Rn)有界性的结论中

参数λ的范围与H?

∞A(Rn)被下述空间所替代时λ的最佳范围仍保持一致

即

被经典Hardy空间或其加权形式

Musielak-Orlicz Hardy空间或各向异性Musielak-Orlicz Hardy空间所替代.

Abstract

Let A be an expansive dilation and ? : Rn× [0

∞) → [0

∞) an anisotropic p-growth function with p ∈(0

1].Let H?

∞A(Rn) be the anisotropic weak Hardy space of Musielak-Orlicz type defined via the grand maximal function.In this article

by using the atomic decomposition of H?

∞A(Rn)

the authors obtain the boundedness of the anisotropic Littlewood-Paley Lusin-area function

the anisotropic g-function and the anisotropic g*λ-function from H?

∞A(Rn) to weak Musielak-Orlicz-type space. Moreover

the range of λ in the boundedness of the anisotropic g*λ-function associated to H?

∞ ∞A(Rn) coincides with the known best conclusions in the case when H?

A(Rn) is replaced by the classical Hardy space or its weighted variant

the Musielak-Orlicz Hardy space or the anisotropic Musielak-Orlicz Hardy space

respectively.

关键词

Keywords

references

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