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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 207–223 | Cite as

Boundedness of Generalized Fractional Integral Operators on Orlicz Spaces Near L1 Over Metric Measure Spaces

  • Daiki Hashimoto
  • Takao OhnoEmail author
  • Tetsu Shimomura
Article
  • 13 Downloads

Abstract

We are concerned with the boundedness of generalized fractional integral operators Iϱ,τ from Orlicz spaces LΦ(X) near L1(X) to Orlicz spaces LΨ(X) over metric measure spaces equipped with lower Ahlfors Q-regular measures, where Φ is a function of the form Φ(r) = rl(r) and l is of log-type. We give a generalization of paper by Mizuta et al. (2010), in the Euclidean setting. We deal with both generalized Riesz potentials and generalized logarithmic potentials.

Keywords

Orlicz space Riesz potential fractional integral metric measure space lower Ahlfors regular 

MSC 2010

31B15 46E30 46E35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Nagasakihokuyodai High SchoolNagasakiJapan
  2. 2.Faculty of EducationOita UniversityDannoharu Oita-cityJapan
  3. 3.Department of Mathematics, Graduate School of EducationHiroshima UniversityHigashi-HiroshimaJapan

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