Some Classical Operators on Vanishing Weighted Orlicz-Morrey Spaces

Abstract

In this paper, we investigate the boundedness of the maximal operator in vanishing weighted Orlicz-Morrey spaces. As an application of this result, we show that these spaces are also invariont with respect to some classical operators of harmonic analysis, such as Riesz potential, fractional maximal operator, Hardy operator.

Keywords

• weighted Orlicz-Morrey spaces
• maximal operator
• Riesz potential
• Hardy operator
• vanishing properties
• applications.

References

1. Alabalik, A., Almeida, A., Samko, S., On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators, Banach J Math Anal., 14(3)(2020), 987–1000.
2. Alabalik, A., Almeida, A., Samko, S., Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators, Math. Methods Appl. Sci., 43(16)(2020), 9375–9386.
3. Almeida, A., Maximal commutators and commutators of potential operators in new vanishing Morrey spaces, Nonlinear Anal., 192(2020).
4. Almeida, A., Samko, S., Approximation in Morrey spaces, J. Funct. Anal., 272(2017), 2392–2411.
5. Deringoz, F., Guliyev, V.S., Samko, S., Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces, Ann. Acad. Sci. Fenn. Math., 40(2015), 535–549.
6. Deringoz, F., Guliyev, V.S., Hasanov, S., Maximal operator and its commutators on generalized weighted Orlicz-Morrey spaces, Tokyo J. Math., 41(2)(2018), 347–369.
7. Deringoz, F., Guliyev, V.S., Nakai, E., Sawano, Y., Shi, M., Generalized fractional maximal and integral operators on Orlicz and generalized Orlicz-Morrey spaces of the third kind, Positivity, 23(2019), 727–757.
8. Deringoz, F., Dorak, K., Mislar, F.A., Some classical operators in a new vanishing generalized Orlicz-Morrey space, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci., 42(4)(2022), 38–45.

9. Fiorenza, A., Krbec, M., Indices of Orlicz spaces and some applications, Comment. Math. Univ. Carolin. 38(3)(1997), 433–451.
10. Gordadze, E., Meskhi, A., Ragusa, M.A., On some extrapolation in generalized grand Morrey spaces with applications to PDEs, Electronic Research Archive, 32(1)(2024), 551–564.
11. Guliyev, V.S., Deringoz, F., Hasanov, J., (Φ,Ψ)-admissible potential operators and their commutators on vanishing Orlicz-Morrey spaces, Collect. Math., 67(2016), 133–153.
12. Guliyev, V.S., Deringoz, F., Riesz potential and its commutators on generalized weighted Orlicz–Morrey spaces, Math. Nachr., 295(2022), 706–724.
13. Kucukaslan, A., Generalized fractional integrals in the vanishing generalized weighted local and global Morrey spaces, Filomat, 37(6)(2023), 1893–1905.
14. Samko, N., Maximal, potential and singular operators in vanishing generalized Morrey spaces, J. Global Optim., 57(4)(2013), 1385–1399.
15. Shi, Y.L., Li, L., Shen, Z.H., Boundedness of p-adic singular integrals and multilinear commutator on Morrey-Herz spaces, Journal of Function Spaces, vol.2023(2023).