Archiv der Mathematik

, Volume 98, Issue 3, pp 253–263 | Cite as

Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces

  • Yoshihiro Mizuta
  • Eiichi NakaiEmail author
  • Yoshihiro Sawano
  • Tetsu Shimomura


The aim of this paper is to give a Gagliardo–Nirenberg inequality for generalized Riesz potentials of functions in Musielak-Orlicz spaces over spaces of homogeneous type.

Mathematics Subject Classification (2010)

Primary 46E35 Secondary 46E30 


Gagliardo–Nirenberg inequality Musielak-Orlicz space Generalized Riesz potentials Variable exponent Space of homogeneous type 


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© Springer Basel AG 2012

Authors and Affiliations

  • Yoshihiro Mizuta
    • 1
  • Eiichi Nakai
    • 2
    Email author
  • Yoshihiro Sawano
    • 3
  • Tetsu Shimomura
    • 4
  1. 1.Department of Mechanical Systems EngineeringHiroshima Institute of TechnologyHiroshimaJapan
  2. 2.Department of MathematicsIbaraki UniversityMitoJapan
  3. 3.Department of MathematicsKyoto UniversityKyotoJapan
  4. 4.Department of Mathematics, Graduate School of EducationHiroshima UniversityHigashi-HiroshimaJapan

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