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Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions

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  • Yoshihiro Mizuta
  • Takao Ohno
  • Tetsu Shimomura
  • Yusuke Yamauchi

Abstract

Riesz decomposition theorem says that superharmonic functions on the punctured unit ball are represented as the sum of generalized (Newtonian) potentials and harmonic functions. In this paper we study growth properties near the origin of spherical means for generalized Riesz potentials of functions satisfying Orlicz conditions in the punctured unit ball.

Suggested Citation

  • Yoshihiro Mizuta & Takao Ohno & Tetsu Shimomura & Yusuke Yamauchi, 2020. "Growth properties for generalized Riesz potentials of functions satisfying Orlicz conditions," Mathematische Nachrichten, Wiley Blackwell, vol. 293(6), pages 1156-1173, June.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:6:p:1156-1173
    DOI: 10.1002/mana.201800569
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