Commutators of Fractional Maximal Operator on Orlicz Spaces
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 516-526.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the present paper, we give necessary and sufficient conditions for the boundedness of commutators of fractional maximal operator on Orlicz spaces. The main advance in comparison with the existing results is that we manage to obtain conditions for the boundedness not in integral terms but in less restrictive terms of supremal operators.
Keywords: Orlicz space, fractional maximal operator, commutator, BMO.
@article{MZM_2018_104_4_a2,
     author = {V. S. Guliev and F. Deringoz and S. G. Hasanov},
     title = {Commutators of {Fractional} {Maximal} {Operator} on {Orlicz} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {516--526},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a2/}
}
TY  - JOUR
AU  - V. S. Guliev
AU  - F. Deringoz
AU  - S. G. Hasanov
TI  - Commutators of Fractional Maximal Operator on Orlicz Spaces
JO  - Matematičeskie zametki
PY  - 2018
SP  - 516
EP  - 526
VL  - 104
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a2/
LA  - ru
ID  - MZM_2018_104_4_a2
ER  - 
%0 Journal Article
%A V. S. Guliev
%A F. Deringoz
%A S. G. Hasanov
%T Commutators of Fractional Maximal Operator on Orlicz Spaces
%J Matematičeskie zametki
%D 2018
%P 516-526
%V 104
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a2/
%G ru
%F MZM_2018_104_4_a2
V. S. Guliev; F. Deringoz; S. G. Hasanov. Commutators of Fractional Maximal Operator on Orlicz Spaces. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 516-526. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a2/

[1] P. Zhang, J. Wu, “Commutators of the fractional maximal function on variable exponent Lebesgue spaces”, Czechoslovak Math. J., 64 (139):1 (2014), 183–197 | DOI | MR

[2] S. Chanillo, “A note on commutators”, Indiana Univ. Math. J., 31:1 (1982), 7–16 | DOI | MR

[3] F. Deringoz, V. S. Guliyev, S. Samko, “Vanishing generalized Orlicz–Morrey spaces and fractional maximal operator”, Publ. Math. Debrecen, 90:1-2 (2017), 125–147 | DOI | MR

[4] J. Garcia-Cuerva, E. Harboure, C. Segovia, J. L. Torrea, “Weighted norm inequalities for commutators of strongly singular integrals”, Indiana Univ. Math. J., 40:4 (1991), 1397–1420 | DOI | MR

[5] J. Bastero, M. Milman, F. J. Ruiz, “Commutators for the maximal and sharp functions”, Proc. Amer. Math. Soc., 128:11 (2000), 3329–3334 | DOI | MR

[6] P. Zhang, J. L. Wu, “Commutators of the fractional maximal functions”, Acta Math. Sinica (Chin. Ser.), 52:6 (2009), 1235–1238 | MR

[7] W. Orlicz, “Über eine gewisse Klasse von Räumen vom Typus $B$”, Bull. Int. Acad. Polon. Sci. A, 1932:8-9 (1932), 207–220 | Zbl

[8] W. Orlicz, “Über Räume ($L^M$)”, Bull. Int. Acad. Polon. Sci. A, 1936 (1936), 93–107 | Zbl

[9] M. M. Rao, Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991 | MR

[10] S. Janson, “Mean oscillation and commutators of singular integral operators”, Ark. Mat., 16:2 (1978), 263–270 | DOI | MR

[11] K.-P. Ho, “Characterization of BMO in terms of rearrangement-invariant Banach function spaces”, Expo. Math., 27:4 (2009), 363–372 | DOI | MR

[12] M. Agcayazi, A. Gogatishvili, K. Koca, R. Mustafayev, “A note on maximal commutators and commutators of maximal functions”, J. Math. Soc. Japan, 67:2 (2015), 581–593 | DOI | MR

[13] V. S. Guliyev, F. Deringoz, S. G. Hasanov, “Riesz potential and its commutators on Orlicz spaces”, J. Inequal. Appl., 2017, Paper No. 75 | MR

[14] V. S. Guliyev, F. Deringoz, S. G. Hasanov, “Fractional maximal function and its commutators on Orlicz spaces”, Anal. Math. Phys., 2017 | DOI