Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind

Abstract

In the present paper, we will characterize the boundedness of the generalized fractional integral operators \(I_{\rho }\) and the generalized fractional maximal operators \(M_{\rho }\) on Orlicz spaces, respectively. Moreover, we will give a characterization for the Spanne-type boundedness and the Adams-type boundedness of the operators \(M_{\rho }\) and \(I_{\rho }\) on generalized Orlicz–Morrey spaces, respectively. Also we give criteria for the weak versions of the Spanne-type boundedness and the Adams-type boundedness of the operators \(M_{\rho }\) and \(I_{\rho }\) on generalized Orlicz–Morrey spaces.

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Acknowledgements

The research of F. Deringoz was partially supported by the Grant of Ahi Evran University Scientific Research Project (FEF.A4.18.019). The research of V. Guliyev was partially supported by the Grant of 1st Azerbaijan–Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/2017-21/01/1) and by the Ministry of Education and Science of the Russian Federation (the Agreement No. 02.a03.21.0008). Eiichi Nakai was supported by Grant-in-Aid for Scientific Research (B), No. 15H03621, Japan Society for the Promotion of Science. Yoshihiro Sawano was supported by Grant-in-Aid for Scientific Research (C) (16K05209), the Japan Society for the Promotion of Science and by Peoples Friendship University of Russia.

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Correspondence to Yoshihiro Sawano.

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Deringoz, F., Guliyev, V.S., Nakai, E. et al. Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz–Morrey spaces of the third kind. Positivity 23, 727–757 (2019). https://doi.org/10.1007/s11117-018-0635-9

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Keywords

  • Generalized fractional maximal function
  • Generalized fractional integral
  • Orlicz spaces
  • Generalized Orlicz-Morrey spaces

Mathematical Subject Classification

  • 42B20
  • 42B25
  • 42B35
  • 46E30