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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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Front. Math. China    2017, Vol. 12 Issue (5) : 1235-1246    https://doi.org/10.1007/s11464-017-0653-0
RESEARCH ARTICLE
Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces
Wei WANG1, Jingshi XU2()
1. School of Sciences, Central South University of Forestry and Technology, Changsha 410004, China
2. School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China
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Abstract

The boundedness of multilinear Calderón-Zygmund operators and their commutators with bounded mean oscillation (BMO) functions in variable exponent Morrey spaces are obtained.

Keywords Multilinear Calderón-Zygmund operator      bounded mean oscillation (BMO) function      commutator      Morrey space      variable exponent     
Corresponding Author(s): Jingshi XU   
Issue Date: 30 September 2017
 Cite this article:   
Wei WANG,Jingshi XU. Multilinear Calderón-Zygmund operators and their commutators with BMO functions in variable exponent Morrey spaces[J]. Front. Math. China, 2017, 12(5): 1235-1246.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0653-0
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I5/1235
1 AlmeidaA, HasanovJ, SamkoS. Maximal and potential operators in variable exponent Morrey spaces. Georgian Math J, 2008, 15: 195–208
2 AlmediaA, HästöP. Besov spaces with variable smoothness and integrability. J Funct Anal, 2010, 258: 1628–1655
https://doi.org/10.1016/j.jfa.2009.09.012
3 Cruz-UribeD V, FiorenzaA. Variable Lebesgue Spaces: Foundations and Harmonic Analysis. Heidelberg: Springer, 2013
https://doi.org/10.1007/978-3-0348-0548-3
4 Cruz-UribeD V, FiorenzaA, MartellC, PérezC. The boundedness of classical operators on variable Lp spaces. Ann Acad Sci Fenn Math, 2006, 31: 239–264
5 DieningL, HarjulehtoP, HästöP, and R°uˇziˇckaM. Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, Vol 2017. Berlin: Springer, 2011
6 DieningL, H¨ast¨oP, RoudenkoS. Function spaces of variable smoothness and integrability. J Funct Anal, 2009, 256: 1731–1768
https://doi.org/10.1016/j.jfa.2009.01.017
7 DongB H, XuJ S. New Herz type Besov and Triebel-Lizorkin spaces with variable exponents. J Funct Spaces Appl, 2012, Article ID 384593, 27 pages
8 FuJ J, XuJ S. Characterizations of Morrey type Besov and Triebel-Lizorkin spaces with variable exponents. J Math Anal Appl, 2011, 381: 280–298
https://doi.org/10.1016/j.jmaa.2011.02.026
9 GrafakosL, TorresR H. Multilinear Calderón-Zygmund theory. Adv Math, 2002, 165: 124–164
https://doi.org/10.1006/aima.2001.2028
10 HästöP. Local-to-global results in variable exponent spaces. Math Res Lett, 2009, 16: 263–278
https://doi.org/10.4310/MRL.2009.v16.n2.a5
11 HoK P. The fractional integral operators on Morrey spaces with variable exponent on unbounded domains. Math Inequal Appl, 2013, 16: 363–373
https://doi.org/10.7153/mia-16-27
12 HoK P. Atomic decomposition of Hardy-Morrey spaces with variable exponents. Ann Acad Sci Fenn Math, 2015, 40: 31–62
https://doi.org/10.5186/aasfm.2015.4002
13 HuangA W, XuJ S. Multilinear singular integrals and commutators in variable exponent Lebesgue spaces. Appl Math J Chinese Univ, 2010, 25: 69–77
https://doi.org/10.1007/s11766-010-2167-3
14 IzukiM. Fractional integrals on Herz-Morrey spaces with variable exponents. Hiroshima Math J, 2010, 40: 343–355
15 IzukiM. Boundedness of commutators on Herz spaces with variable exponents. Rend Circ Mat Palermo, 2010, 59: 199–213
https://doi.org/10.1007/s12215-010-0015-1
16 Kov´aˇcikO, ŔakosńıkJ. On spaces Lp(x) and Wk,p(x). Czechoslovak Math J, 1991, 41(4): 592–618
17 NakaiE, SawanoY. Hardy spaces with variable exponents and generalized Campanato spaces. J Funct Anal, 2012, 262: 3665–3748
https://doi.org/10.1016/j.jfa.2012.01.004
18 ShiC, XuJ S. Herz type Besov and Triebel-Lizorkin spaces with variable exponent. Front Math China, 2013, 8: 907–921
https://doi.org/10.1007/s11464-012-0248-8
19 TangC Q, WuQ, XuJ S. Commutators of multilinear Calderón-Zygmund operator and BMO functions in Herz-Morrey spaces with variable exponents. J Funct Spaces Appl, 2014, Article ID 162518, 12 pages
20 TaoX, ZhangH. On the boundedness of multilinear operators on weighted Herz-Morrey spaces. Taiwanese J Math, 2011, 15: 1527–1543
https://doi.org/10.11650/twjm/1500406362
21 WangW, XuJ S. Commutators of multilinear singular integrals with Lipschits functions. Commun Math Res, 2009, 25: 318–328
22 XuJ S. Generalized commutators of multilinear singular integrals. Proc A Razmadze Math Inst, 2006, 142: 109–122
23 XuJ S. Multilinear commutators of multilinear singular integrals. Acta Math Sinica (Chin Ser), 2008, 51: 1021–1034 (in Chinese)
24 XuJ S. Variable Besov and Triebel-Lizorkin spaces. Ann Acad Sci Fenn Math, 2008, 33: 511–522
25 XuJ S. Admissibility for topological degree of Besov and Triebel-Lizorkin spaces with variable integrability. Georgian Math J, 2011, 18: 365–375
26 ZhouJ, CaoY H, LiL. Estimates of commutators for multilinear operators on Herztype spaces. Appl Math J Chinese Univ, 2010, 25(2): 177–184
https://doi.org/10.1007/s11766-010-1888-7
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