@article{He2022, 
author = {Suixin He and Shuangping Tao},
title = {Boundedness of some operators on grand generalized Morrey spaces over non-homogeneous spaces},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {1000-1014},
keywords = {non-doubling measure, maximal operator, fractional integral operator, θ-type Calderón-Zygmund operator, grand generalized Morrey space},
url = {https://www.sciopen.com/article/10.3934/math.2022060},
doi = {10.3934/math.2022060},
abstract = {The aim of this paper is to obtain the boundedness of some operator on grand generalized Morrey space              L              μ              p      )      ,      φ      ,      ϕ        (  G  ) over non-homogeneous spaces, where    G  ⊂              R              n       is a bounded domain. Under assumption that functions    φ and    ϕ satisfy certain conditions, the authors prove that the Hardy-Littlewood maximal operator, fractional integral operators and    θ-type Calderón-Zygmund operators are bounded on the non-homogeneous grand generalized Morrey space              L              μ              p      )      ,      φ      ,      ϕ        (  G  ). Moreover, the boundedness of commutator    [  b  ,      T          θ              G        ] which is generated by    θ-type Calderón-Zygmund operator        T          θ       and    b  ∈      R    B    M    O    (  μ  ) on spaces              L              μ              p      )      ,      φ      ,      ϕ        (  G  ) is also established.}
}