Compactness of Commutators for Riesz Potential on Local Morrey-type spaces.

被引：1
|
作者：
Matin, D. T. [1 ]
Akhazhanov, T. B. [1 ]
Adilkhanov, A. [1 ]
机构：
[1] LN Gumilyov Eurasian Natl Univ, Astana, Kazakhstan
来源：
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS | 2023年 / 110卷 / 02期
关键词：
Compactness; Commutators; Riesz Potential; Local Morrey-type spaces; CLASSICAL OPERATORS; RECENT PROGRESS; REAL ANALYSIS; BOUNDEDNESS;
D O I：
10.31489/2023M2/93-103
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The paper considers Morrey-type local spaces from LMwp & theta; The main work is the proof of the commutator compactness theorem for the Riesz potential [b, I & alpha;] in local Morrey-type spaces from LMp & theta;w1 to LMw2 q & theta; . We also give new sufficient conditions for the commutator to be bounded for the Riesz potential [b, I & alpha;] in local Morrey-type spaces from LMp & theta;w1 to LMw2 q & theta; . In the proof of the commutator compactness theorem for the Riesz potential, we essentially use the boundedness condition for the commutator for the Riesz potential [b, I & alpha;] in local Morrey-type spaces LMwp & theta;, and use the sufficient conditions from the theorem of precompactness of sets in local spaces of Morrey type LMwp & theta;. In the course of proving the commutator compactness theorem for the Riesz potential, we prove lemmas for the commutator ball for the Riesz potential [b, I & alpha;]. Similar results were obtained for global Morrey-type spaces GMwp & theta; and for generalized Morrey spaces Mpw.
引用
收藏
页码：93 / 103
页数：11
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