Littlewood-Paley theory for variable exponent Lebesgue spaces and Gagliardo-Nirenberg inequality for Riesz potentials

• Mizuta Yoshihiro

  Department of Mathematics, Graduate School of Science, Hiroshima University

• Nakai Eiichi

  Department of Mathematics, Osaka Kyoiku University

• Sawano Yoshihiro

  Department of Mathematics, Kyoto University

• Shimomura Tetsu

  Department of Mathematics, Graduate School of Education, Hiroshima University

Abstract

Our aim in this paper is to prove the Gagliardo-Nirenberg inequality for Riesz potentials of functions in variable exponent Lebesgue spaces, which are called Musielak-Orlicz spaces with respect to Φ(x,t) = t^p(x)(log(c₀ + t))^q(x) for t > 0 and x ∈ ℝⁿ, via the Littlewood-Paley decomposition.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 65 (2), 633-670, 2013

  The Mathematical Society of Japan

Keywords

• Gagliardo-Nirenberg inequality
• Riesz potentials
• variable exponents
• Musielak-Orlicz spaces
• Littlewood-Paley theory

Details

• CRID: 1390001205116119296
• NII Article ID: 10031177293
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/06520633
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• NDL BIB ID: 024429226
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I024429226
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed