Geodesic
A Note on the Boundedness of Iterated Commutators of Multilinear Operators
Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 48-54 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We show that the symbol function belonging to $BMO$ space is not a necessary condition for the boundedness of the iterated commutator acting on a product of Lebesgue spaces.
Keywords: BMO function, boundedness, commutator, Hardy–Littlewood maximal function
Mots-clés : Lebesgue space. 
@article{MZM_2022_112_1_a3,
     author = {Dinghuai Wang},
     title = {A {Note} on the {Boundedness} of {Iterated} {Commutators} of {Multilinear} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {48--54},
     year = {2022},
     volume = {112},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a3/}
}
TY  - JOUR
AU  - Dinghuai Wang
TI  - A Note on the Boundedness of Iterated Commutators of Multilinear Operators
JO  - Matematičeskie zametki
PY  - 2022
SP  - 48
EP  - 54
VL  - 112
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a3/
LA  - ru
ID  - MZM_2022_112_1_a3
ER  - 
%0 Journal Article
%A Dinghuai Wang
%T A Note on the Boundedness of Iterated Commutators of Multilinear Operators
%J Matematičeskie zametki
%D 2022
%P 48-54
%V 112
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a3/
%G ru
%F MZM_2022_112_1_a3
Dinghuai Wang. A Note on the Boundedness of Iterated Commutators of Multilinear Operators. Matematičeskie zametki, Tome 112 (2022) no. 1, pp. 48-54. http://geodesic.mathdoc.fr/item/MZM_2022_112_1_a3/

[1] R. A. Devore, R. C. Sharpley, Maximal functions measuring smoothness, Mem. Amer. Math. Soc., 47, Amer. Math. Soc., Providence, RI, 1984 | MR

[2] S. Janson, M. Taibleson, G. Weiss, “Elementary characterization of the Morrey–Campanato spaces”, Harmonic Analysis, Lecture Notes in Math., 992, Springer, Berlin, 1983, 101–114 | DOI | MR

[3] D. H. Wang, J. Zhou, Z. D. Teng, “A Note on Campanato Spaces and Their Applications”, Math. Notes, 103:3 (2018), 483–489 | DOI | MR | Zbl

[4] R. Coifman, R. Rochberg, G. Weiss, “Factorization theorems for Hardy spaces in several variables”, Ann. of Math., 103 (1976), 611–635 | DOI | MR | Zbl

[5] C. Pérez, R. H. Torres, “Sharp maximal function estimates for multilinear singular integrals”, Harmonic Analysis at Mount Holyoke, Contemp. Math., 320, Amer. Math. Soc., Providence, RI, 2003, 323–331 | MR

[6] L. Tang, “Weighted estimates for vector-valued commutators of multilinear operators”, Proc. Roy. Soc. Edinburgh Sect. A, 138:4 (2008), 897–922 | DOI | MR

[7] A. K. Lerner, S. Ombrosi, C. Pérez, R. H. Torres, R. Trujillo-González, “New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory”, Adv. Math., 220 (2009), 1222–1264 | DOI | MR | Zbl

[8] L. Chaffee, “Characterizations of BMO through commutators of bilinear singular integral operators”, Proc. Roy. Soc. Edinburgh Sect. A, 146:6 (2016), 1159–1166 | DOI | MR | Zbl

[9] S. B. Wang, J. B. Pan, Y. S. Jiang, “Necessary and sufficient conditions for boundedness of commutators of multilinear fractional integral operators”, Acta Math. Sci. Ser. A (Chinese Ed.), 35:6 (2015), 1106–1114 | MR | Zbl

[10] D. H. Wang, J. Zhou, Z. D. Teng, “Characterization of CMO via compactness of the commutators of bilinear fractional integral operators”, Anal. Math. Phys., 9:4 (2019), 1669–1688 | DOI | MR | Zbl

[11] C. Fefferman, E. M. Stein, “$H^{p}$ spaces of several variables”, Acta Math., 129:3-4 (1972), 137–193 | DOI | MR | Zbl

[12] P. Zhang, “Multiple Weighted estimates for commutators of Multilinear maximal function”, Acta Math. Sin. (Engl. Ser.), 31:6 (2015), 973–994 | DOI | MR | Zbl

[13] C. Pérez, G. Pradolini, R. H. Torres, R. Trujillo-González, “End-points estimates for iterated commutators of multilinear singular integrals”, Bull. London Math. Soc., 46:1 (2014), 26–42 | DOI | MR

[14] C. Pérez, R. Trujillo-González, “Sharp weighted estimates for multilinear commutators”, J. London Math. Soc. (2), 65:3 (2002), 672–692 | DOI | MR