Bochner-Riesz算子交換子在加權(quán)Morrey空間上的有界性

張姍姍,瞿萌,束立生

(安徽師范大學(xué)數(shù)學(xué)計(jì)算機(jī)科學(xué)學(xué)院,安徽蕪湖 241003)

Bochner-Riesz算子交換子在加權(quán)Morrey空間上的有界性

張姍姍,瞿萌,束立生

(安徽師范大學(xué)數(shù)學(xué)計(jì)算機(jī)科學(xué)學(xué)院,安徽蕪湖 241003)

運(yùn)用了Sharp極大函數(shù)估計(jì)的方法證明了當(dāng)權(quán)函數(shù)滿足一定條件時(shí),Bochner-Riesz算子與加權(quán)BMO函數(shù)生成的交換子在加權(quán)Morrey空間上的有界性.

Bochner-Riesz算子;加權(quán)Morrey空間;加權(quán)BMO空間

1 引言及相關(guān)定義

經(jīng)典的Morrey空間Lp,λ首先是由Morrey[1]在研究二階橢圓型偏微分方程解的局部性質(zhì)時(shí)所引進(jìn)的.2009年,Komori和Shirai[2]建立了加權(quán)Morrey空間Lp,κ(ω)并且研究了調(diào)和分析中一些主要算子,比如Hardy-Littlewood極大算子,Calder′on-Zygmund奇異積分算子以及分?jǐn)?shù)次積分算子在這些加權(quán)Morrey空間上的有界性問(wèn)題.在?n(n≥2)中階為δ＞0 的Bochner-Riesz算子起初是通過(guò)Fourier變換,對(duì)Schwartz函數(shù)來(lái)定義的,

這些算子首先是由Bochner引進(jìn)的,它們與多重Fourier級(jí)數(shù)的求和密切相關(guān)并且在調(diào)和分析的研究中起著很重要的作用.設(shè)b是?n上的一個(gè)局部可積函數(shù),對(duì)于任意給定的R＞0, b和所生成的交換子定義如下:

2 主要結(jié)果及證明

從而完成了定理的證明.

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Boundedness of the commutator of Bochner-Riesz operators on weighted Morrey spaces

Zhang Shanshan,Qu Meng,Shu Lisheng
(College of Mathematics and Computer Science,Anhui Normal University,Wuhu241003,China)

In this paper,we use a method of sharp maximal function to show the boundedness of commutator generated by Bochner-Riesz operators and weighted BMO function on the weighted Morrey spaces under appropriate conditions on the weight.

Bochner-Riesz operators,weighted Morrey spaces,weighted BMO spaces

O174.2

A

1008-5513(2013)02-0214-07

10.3969/j.issn.1008-5513.2013.02.016

2012-12-05.

安徽省高校自然科學(xué)項(xiàng)目(KJ2011A138).

張姍姍(1989-),碩士生,研究方向:調(diào)和分析.

2010 MSC:42B25