ON MODIFIED ORLICZ-MORREY SPACES
DOI:
https://doi.org/10.58225/sw.2025.2-73-78Keywords:
Orlicz spaces, modified Morrey spaces, modified Orlicz-Morrey spaces, third versionAbstract
In this article, we discussed the third version of weak modified Orlicz-Morrey spaces, which is an enlargement of the third version of (strong) modified Orlicz-Morrey spaces. Similar to its first version and second version, the third version of strong and weak modified Orlicz-Morrey space is considered as a generalization of strong and weak Orlicz spaces and strong and weak
modified Morrey spaces. This study investigated some properties of the third version modified Orlicz-Morrey spaces.
- Views
- 325
- Downloads
- 221
References
1. Aykol C, Armutcu H, Omarova MN. Maximal commutator and commutator of maximal function on modified Morrey spaces. Transactions of the National Academy of Sciences of Azerbaijan. Series
of Physical-Technical and Mathematical Sciences. Mathematics. 2016;36(1):29–35
2. Cianchi A. Strong and weak type inequalities for some classical operators in Orlicz spaces. Journal of the London Mathematical Society. 1999;60(1):187–202
3. Deringoz F, Guliyev VS, Samko S. Boundedness of maximal and singular operators on generalized Orlicz–Morrey spaces. In: Operator Theory, Operator Algebras and Applications.
Operator Theory: Advances and Applications. Vol. 242. Basel: Birkhäuser; 2014. p. 139–158
4. Guliyev VS. Integral operators on function spaces on homogeneous groups and on domains in ℝⁿ.Doctoral dissertation. Moscow: Steklov Mathematical Institute; 1994. 329 p. (In Russian)
5. Guliyev VS. Function spaces, integral operators and two weighted inequalities on homogeneous groups. Some applications. Baku: Casioglu; 1999. 332 p. (In Russian)
6. Guliyev VS, Hasanov JJ, Zeren Y. Necessary and sufficient conditions for the boundedness of the Riesz potential in modified Morrey spaces. Journal of Mathematical Inequalities. 2011;5(4):491–506
7. Guliyev VS, Hasanov SG, Sawano Y, Noi T. Non-smooth atomic decompositions for generalized Orlicz–Morrey spaces of the third kind. Acta Applicandae Mathematicae. 2016;145:133–174
8. Hencl S, Kleprlik L. Composition of qqq-quasiconformal mappings and functions in Orlicz–Sobolev spaces. Illinois Journal of Mathematics. 2012;56(3):931–955
9. Kita H. On maximal functions in Orlicz spaces. Proceedings of the American Mathematical Society. 1996;124:3019–3025
10. Kita H. On Hardy–Littlewood maximal functions in Orlicz spaces. Mathematische Nachrichten.1997;183:135–155
11. Nakai E. Generalized fractional integrals on Orlicz–Morrey spaces. In: Banach and Function Spaces (Kitakyushu, 2003). Yokohama: Yokohama Publishers; 2004. p. 323–333
12. Orlicz W. Über eine gewisse Klasse von Räumen vom Typus B. Bulletin de l’Académie Polonaise des Sciences. Série A. 1932:207–220; reprinted in: Collected Papers. Warsaw: PWN;
1988. p. 217–230
13. Orlicz W. Über Räume (LM). Bulletin de l’Académie Polonaise des Sciences. Série A. 1936:93–107; reprinted in: Collected Papers. Warsaw: PWN; 1988. p. 345–359.
14. Sawano Y, Sugano S, Tanaka H. Orlicz–Morrey spaces and fractional operators. Potential Analysis. 2012;36(4):517–556
Published
Issue
Section
License
Copyright (c) 2025 Ali Akbulut, Vagif Guliyev, Mehriban Omarova (Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.


