\((\Phi ,\Psi )\) -admissible potential operators and their commutators on vanishing Orlicz-Morrey spaces

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• 作者：Vagif S. Guliyev ; Fatih Deringoz ; Javanshir J. Hasanov
• 关键词：Vanishing generalized Orlicz ; Morrey space ; $$(\Phi ; \Psi )$$ ( Φ ; Ψ ) ; admissible potential operators ; Fractional maximal operator ; Riesz potential ; Commutator ; BMO ; Primary 42B20 ; 42B25 ; 42B35 ; 46E30
• 刊名：Collectanea Mathematica
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：67
• 期：1
• 页码：133-153
• 全文大小：552 KB
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• 作者单位：Vagif S. Guliyev (1) (2)
  Fatih Deringoz (1)
  Javanshir J. Hasanov (2)
  
  1. Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
  2. Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, F. Agayev St. 9, Baku, 1141, Azerbaijan
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Analysis
  Applications of Mathematics
  Geometry
  
• 出版者：Springer Milan
• ISSN：2038-4815

文摘

We study the boundedness of \((\Phi ,\Psi )\)-admissible potential operators and their commutators on vanishing generalized Orlicz-Morrey spaces \(VM_{\Phi ,\varphi }(\mathbb {R}^n)\) including their weak versions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Riesz potential, fractional maximal operator and so on. In all the cases the conditions for the boundedness are given in terms of Zygmund-type integral inequalities involving the Young functions \(\Phi \), \(\Psi \) and the function \(\varphi (x,r)\) defining the space, without assuming any monotonicity property of \(\varphi (x,r)\) on \(r\). Keywords Vanishing generalized Orlicz-Morrey space \((\Phi , \Psi )\)-admissible potential operators Fractional maximal operator Riesz potential Commutator BMO