Orlicz-fractional maximal operators on weighted L^p spaces
Orlicz-fractional maximal operators on weighted L^p spaces
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DOI：
10.7153/jmi-2019-13-26
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发表时间：
2019
影响因子：
2.9
通讯作者：
Takeshi Iida;Y. Sawano
中科院分区：
文献类型：
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作者：
Takeshi Iida;Y. Sawano
。在Orlicz空间的尺度上给出了Lebesgue空间上权范数不等式成立的充要条件，该条件推广了分数极大算子。关于Orlicz极大算子的一个类似的论点是由P´erez提出的，他推广了费弗曼-斯坦不等式。主要结果是得到了Sawyer型和Hardy-Littlewood-Sobolev型分数极大算子的Fefferman-Stein不等式。本文证明了Orlicz极大算子的L - p有界性和Fefferman-Stein型不等式本质上等价于分数阶Orlicz极大算子的Saywer型不等式。这些不等式比Hardy-Littlewood-Sobolev型不等式更强。更一般地，我们考虑了普通和广义分数阶Orlicz极大算子的几个混合强型不等式。作为应用，我们研究了换易子[b， I α]的权模不等式，其中b∈BMO (rn)， I α是分数阶积分算子。
. Necessary and suf fi cient conditions for weight norm inequalities on Lebesgue spaces to hold are given in the scale of Orlicz spaces for the fractional Orlicz maximal operators which generalizes the fractional maximal operators. A similar argument for the Orlicz maximal op- erators is due to P´erez, who generalizes for the Fefferman–Stein inequality. The main result is the Fefferman–Stein inequality for the fractional maximal operators of the Sawyer type and the Hardy–Littlewood–Sobolev type. In this paper, we establish that the L p -boundedness and the Fefferman–Stein type inequality of Orlicz maximal operator are essentially equivalent to the Saywer type inequality for the fractional Orlicz maximal operators. These inequalities are stronger than the Hardy–Littlewood–Sobolev type inequalities. More generally, we consider sev- eral mixed strong type inequalities for the ordinary and generalized fractional Orlicz maximal operators. As an application, we investigate the weight norm inequalities of the commutator [ b , I α ] , where b ∈ BMO ( R n ) , and I α the fractional integral operator.