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Revista Matemática Complutense

, Volume 29, Issue 1, pp 59–90 | Cite as

Generalized fractional maximal operators and vector-valued inequalities on generalized Orlicz–Morrey spaces

  • Denny Ivanal Hakim
  • Eiichi Nakai
  • Yoshihiro Sawano
Article

Abstract

In the present paper, we shall give a necessary and sufficient condition for the weak/strong boundedness of generalized fractional maximal operators on generalized Orlicz–Morrey spaces. We also give necessary and sufficient conditions for the vector-valued inequalities of the Hardy–Littlewood maximal operator, generalized fractional maximal operators and singular integral operators on these function spaces.

Keywords

Generalized fractional maximal operators Generalized Orlicz–Morrey spaces Hardy–Littlewood maximal operator Singular integral operators Vector-valued inequalities 

Mathematics Subject Classification

42B35 42B25 

Notes

Acknowledgments

The authors are thankful to anonymous referees for their careful reading of our paper and some fruitful comments. The second author was supported by Grant-in-Aid for Scientific Research (C), No. 24540159 and Grant-in-Aid for Scientific Research (B), No. 15H03621, Japan Society for the Promotion of Science. The third author was supported by Grant-in-Aid for Young Scientists (B), No. 24740085, Japan Society for the Promotion of Science.

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Copyright information

© Universidad Complutense de Madrid 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Information SciencesTokyo Metropolitan UniversityHachiojiJapan
  2. 2.Department of MathematicsIbaraki UniversityMitoJapan

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