An extension of the characterization of CMO and its application to compact commutators on Morrey spaces

• Arai Ryutaro

  Department of Mathematics Ibaraki University

• Nakai Eiichi

  Department of Mathematics Ibaraki University

Bibliographic Information

Other Title

• An extension of the characterization of $\mathrm{CMO}$ and its application to compact commutators on Morrey spaces

Abstract

In 1978 Uchiyama gave a proof of the characterization of CMO(ℝ^𝑛) which is the closure of 𝐶^∞_comp(ℝ^𝑛) in BMO(ℝ^𝑛). We extend the characterization to the closure of 𝐶^∞_comp(ℝ^𝑛) in the Campanato space with variable growth condition. As an application we characterize compact commutators [𝑏, 𝑇] and [𝑏, 𝐼_𝛼] on Morrey spaces with variable growth condition, where 𝑇 is the Calderón–Zygmund singular integral operator, 𝐼_𝛼 is the fractional integral operator and 𝑏 is a function in the Campanato space with variable growth condition.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 72 (2), 507-539, 2020

  The Mathematical Society of Japan

Keywords

• Campanato space
• Morrey space
• variable growth condition
• singular integral
• fractional integral
• commutator

Details

• CRID: 1390003825176041984
• NII Article ID: 130007834784
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/81458145
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 030377363
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I030377363
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed