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Revista Matemática Complutense

, Volume 29, Issue 2, pp 295–340 | Cite as

Interpolation of generalized Morrey spaces

  • Denny Ivanal HakimEmail author
  • Yoshihiro Sawano
Article

Abstract

In this paper, we shall establish a theory of interpolation of generalized Morrey spaces. We use the complex interpolation methods. Our results extend the interpolation results for Morrey spaces which are discussed by Lu et al. (Can Math Bull 57:598–608, 2014), and also Lemarié-Rieusset (2014). We establish the interpolation of generalized weak Morrey spaces, generalized Orlicz–Morrey spaces and generalized weak Orlicz–Morrey spaces. We also consider the closure of the functions which are essentially bounded and have compact support. The second interpolation of such spaces will yield a class of closed spaces; we describe the second interpolation of the closure of the functions which are essentially bounded and have compact support. This result will carry over to generalized Morrey spaces, generalized weak Morrey spaces, generalized Orlicz–Morrey spaces and generalized weak Orlicz–Morrey spaces. We also give several examples that explain the subtlety of proving the interpolation of Morrey spaces.

Keywords

Morrey spaces Orlicz–Morrey spaces Complex interpolation functors 

Mathematics Subject Classification

46B70 42B35 46B26 

Notes

Acknowledgments

The authors are thankful to Professor Wen Yuan for the discussion with the second author. The authors are also grateful to Dr. Shohei Nakamura for his pointing out our mistake in the assumptions in Lemmas 8 and 16.

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Copyright information

© Universidad Complutense de Madrid 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Information SciencesTokyo Metropolitan UniversityHachiojiJapan

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