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Collectanea Mathematica

, Volume 69, Issue 3, pp 377–394 | Cite as

Variable exponent weighted norm inequality for generalized Riesz potentials on the unit ball

  • Fumi-Yuki Maeda
  • Yoshihiro Mizuta
  • Tetsu Shimomura
Article

Abstract

Our aim in this paper is to establish variable exponent weighted norm inequalities for generalized Riesz potentials on the unit ball via norm inequalities in variable exponent non-homogeneous central Herz–Morrey spaces on the unit ball. As an application, we shall show Sobolev-type integral representation for a \(C^1\)-function on \({\mathbb R}^N{\setminus } \{0\}\) which vanishes outside the unit ball.

Keywords

Weighted norm inequality Variable exponent Sobolev’s inequality Riesz potentials Sobolev integral representation 

Mathematics Subject Classification

Primary 46E30 31B15 

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Copyright information

© Universitat de Barcelona 2017

Authors and Affiliations

  • Fumi-Yuki Maeda
    • 1
  • Yoshihiro Mizuta
    • 2
  • Tetsu Shimomura
    • 3
  1. 1.4-24 Furue-higashi-machi, Nishi-kuHiroshimaJapan
  2. 2.4-13-11 Hachi-Hon-Matsu-MinamiHigashi-HiroshimaJapan
  3. 3.Department of Mathematics, Graduate School of EducationHiroshima UniversityHigashi-HiroshimaJapan

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