加权变量Hardy空间上范数不等式的一个新方法

IF 0.9 4区数学 Q2 Mathematics

Annales Academiae Scientiarum Fennicae-Mathematica Pub Date : 2019-02-05 DOI:10.5186/aasfm.2020.4526

D. Cruz-Uribe, Kabe Moen, H. Nguyen

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引用次数: 11

摘要

给出了加权和变指数Hardy空间上分数和奇异积分算子Hardy空间估计的新证明。我们的证明由几个相互关联的思想组成:根据$L^\infty$原子的有限原子分解，极大算子和其他算子的向量值不等式，以及Rubio de Francia外推。这些估计中的许多不是新的，但我们给出了新的和实质上更简单的证明，这反过来又大大简化了哈代空间不等式的证明。

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A new approach to norm inequalities on weighted and variable Hardy spaces

We give new proofs of Hardy space estimates for fractional and singular integral operators on weighted and variable exponent Hardy spaces. Our proofs consist of several interlocking ideas: finite atomic decompositions in terms of $L^\infty$ atoms, vector-valued inequalities for maximal and other operators, and Rubio de Francia extrapolation. Many of these estimates are not new, but we give new and substantially simpler proofs, which in turn significantly simplifies the proofs of the Hardy spaces inequalities.

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来源期刊

Annales Academiae Scientiarum Fennicae-Mathematica 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Annales Academiæ Scientiarum Fennicæ Mathematica is published by Academia Scientiarum Fennica since 1941. It was founded and edited, until 1974, by P.J. Myrberg. Its editor is Olli Martio. AASF publishes refereed papers in all fields of mathematics with emphasis on analysis.