Abstract
We introduce grand Morrey spaces and establish the boundedness of Hardy–Littlewood maximal, Calderón–Zygmund and potential operators in these spaces. In our case the operators and grand Morrey spaces are defined on quasi-metric measure spaces with doubling measures. The results are new even for Euclidean spaces.
Acknowledgements
The author expresses his gratitude to Prof V. Kokilashvili for drawing his attention to the problems studied in this work and helpful comments and remarks. The author is also thankful to the referees for their useful remarks. This work was partially supported by the Georgian National Science Foundation Grant No. GNSF/ST09_23_3-100.