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Vanishing exponential integrability for Riesz potentials in Morrey–Orlicz spaces

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  • Yoshihiro Mizuta
  • Tetsu Shimomura

Abstract

Our aim in this note is to establish exponential integrability and vanishing exponential integrability for Riesz potentials of functions in Morrey–Orlicz spaces. Our work generalizes results by Adams and Hurri‐Syrjänen (2003) and the authors (2007) from Orlicz case. We also discuss the size of the exceptional sets by using a capacity and Hausdorff measure.

Suggested Citation

  • Yoshihiro Mizuta & Tetsu Shimomura, 2024. "Vanishing exponential integrability for Riesz potentials in Morrey–Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 297(1), pages 110-125, January.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:1:p:110-125
    DOI: 10.1002/mana.202200198
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