Generalized Morrey Spaces – Revisited

  • Ali Akbulut

    Ahi Evran University, Kirsehir, Turkey
  • Vagif Sabir Guliyev

    Ahi Evran University, Kirsehir, Turkey
  • Takahiro Noi

    Tokyo Metropolitan University, Japan
  • Yoshihiro Sawano

    Tokyo Metropolitan University, Japan


The generalized Morrey space was defined by Mizuhara 1991 and Nakai in 1994. It is equipped with a parameter and a function . Our experience shows that is easy to handle when . However, when , the function space is difficult to handle as many examples show. We propose a way to deal with for , in particular, to obtain some estimates of the Hardy–Littlewood maximal operator on these spaces. Especially, the vector-valued estimates obtained in the earlier papers are refined. The key tool is the weighted dual Hardy operator. Much is known on the weighted dual Hardy operator.

Cite this article

Ali Akbulut, Vagif Sabir Guliyev, Takahiro Noi, Yoshihiro Sawano, Generalized Morrey Spaces – Revisited. Z. Anal. Anwend. 36 (2017), no. 1, pp. 17–35

DOI 10.4171/ZAA/1577