Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

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• 作者：Ka Luen Cheung (1)
  Kwok-Pun Ho (1)
  
• 关键词：block space ; variable exponent analysis ; Hardy ; Littlewood maximal operator ; 42B25 ; 46E30
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：64
• 期：1
• 页码：159-171
• 全文大小：173 KB
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• 作者单位：Ka Luen Cheung (1)
  Kwok-Pun Ho (1)
  
  1. Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, Hong Kong, China
  
• ISSN：1572-9141

文摘

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.