1 |
E. Nakai and Y. Sawano, Hardy spaces with variable exponents and generalized Campanato spaces, J. Funct. Anal. 262 (2012), no. 9, 3665-3748. https://doi.org/10.1016/j.jfa.2012.01.004
DOI
|
2 |
W. Orlicz, Uber konjugierte Exponentenfolgen, Stud. Math. 3 (1931), 200-211.
DOI
|
3 |
C. Perez and R. H. Torres, Sharp maximal function estimates for multilinear singular integrals, in Harmonic analysis at Mount Holyoke (South Hadley, MA, 2001), 323-331, Contemp. Math., 320, Amer. Math. Soc., Providence, RI, 2003. https://doi.org/10.1090/conm/320/05615
DOI
|
4 |
J. Tan, Z. Liu, and J. Zhao, On some multilinear commutators in variable Lebesgue spaces, J. Math. Inequal. 11 (2017), no. 3, 715-734. https://doi.org/10.7153/jmi2017-11-57
DOI
|
5 |
J. Tan and J. Zhao, Rough fractional integrals and its commutators on variable Morrey spaces, C. R. Math. Acad. Sci. Paris 353 (2015), no. 12, 1117-1122. https://doi.org/10.1016/j.crma.2015.09.024
DOI
|
6 |
A. Uchiyama, On the compactness of operators of Hankel type, Tohoku Math. J. (2) 30 (1978), no. 1, 163-171. https://doi.org/10.2748/tmj/1178230105
DOI
|
7 |
H. Wang and Z. Liu, The wavelet characterization of Herz-type Hardy spaces with variable exponent, Ann. Funct. Anal. 3 (2012), no. 1, 128-141. https://doi.org/10.15352/afa/1399900030
DOI
|
8 |
Y. Zhu and L. Liu, Weighted sharp boundedness for multilinear commutators of singular integral on spaces of homogeneous type, Vietnam J. Math. 39 (2011), no. 4, 381-390.
|
9 |
D. Yang, C. Zhuo, and W. Yuan, Triebel-Lizorkin type spaces with variable exponents, Banach J. Math. Anal. 9 (2015), no. 4, 146-202. https://doi.org/10.15352/bjma/09-4-9
DOI
|
10 |
X. Fu, D. Yang, and W. Yuan, Generalized fractional integrals and their commutators over non-homogeneous metric measure spaces, Taiwanese J. Math. 18 (2014), no. 2, 509-557. https://doi.org/10.11650/tjm.18.2014.3651
DOI
|
11 |
L. Liu, D. Chang, X. Fu, and D. Yang, Endpoint boundedness of commutators on spaces of homogeneous type, Appl. Anal. 96 (2017), no. 14, 2408-2433. https://doi.org/10.1080/00036811.2017.1341628
DOI
|
12 |
D. V. Cruz-Uribe and A. Fiorenza, Variable Lebesgue Spaces, Applied and Numerical Harmonic Analysis, Birkhauser/Springer, Heidelberg, 2013. https://doi.org/10.1007/978-3-0348-0548-3
DOI
|
13 |
R. R. Coifman, R. Rochberg, and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), no. 3, 611-635. https://doi.org/10.2307/1970954
DOI
|
14 |
D. Cruz-Uribe and L.-A. D. Wang, Variable Hardy spaces, Indiana Univ. Math. J. 63 (2014), no. 2, 447-493. https://doi.org/10.1512/iumj.2014.63.5232
DOI
|
15 |
G. Lu, S. Lu, and D. Yang, Singular integrals and commutators on homogeneous groups, Anal. Math. 28 (2002), no. 2, 103-134. https://doi.org/10.1023/A:1016568918973
DOI
|
16 |
M. Bramanti, Commutators of integral operators with positive kernels, Matematiche (Catania) 49 (1994), no. 1, 149-168.
|
17 |
M. Bramanti and M. C. Cerutti, Commutators of singular integrals and fractional integrals on homogeneous spaces, in Harmonic analysis and operator theory (Caracas, 1994), 81-94, Contemp. Math., 189, Amer. Math. Soc., Providence, RI, 1995. https://doi.org/10.1090/conm/189/02257
DOI
|
18 |
L. Chaffee, Commutators of multilinear singular integral operators with pointwise multiplication, Thesis (Ph.D.), University of Kansas, 2015.
|
19 |
S. Chanillo, A note on commutators, Indiana Univ. Math. J. 31 (1982), no. 1, 7-16. https://doi.org/10.1512/iumj.1982.31.31002
DOI
|
20 |
X. Chen and Q. Xue, Weighted estimates for a class of multilinear fractional type operators, J. Math. Anal. Appl. 362 (2010), no. 2, 355-373. https://doi.org/10.1016/j.jmaa.2009.08.022
DOI
|
21 |
D. Cruz-Uribe, A. Fiorenza, J. M. Martell, and C. Perez, The boundedness of classical operators on variable Lp spaces, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 1, 239-264.
|
22 |
X. T. Duong, H. Li, J. Li, and B. D. Wick, Lower bound of Riesz transform kernels and commutator theorems on stratified nilpotent Lie groups, J. Math. Pures Appl. (9) 124 (2019), 273-299. https://doi.org/10.1016/j.matpur.2018.06.012
DOI
|
23 |
J. Fang and J. Zhao, Variable Hardy spaces on the Heisenberg group, Anal. Theory Appl. 32 (2016), no. 3, 242-271. https://doi.org/10.4208/ata.2016.v32.n3.4
DOI
|
24 |
G. B. Folland and E. M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, 28, Princeton University Press, Princeton, NJ, 1982.
|
25 |
L. Grafakos and R. H. Torres, Multilinear Calderon-Zygmund theory, Adv. Math. 165 (2002), no. 1, 124-164. https://doi.org/10.1006/aima.2001.2028
DOI
|
26 |
S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Mat. 16 (1978), no. 2, 263-270. https://doi.org/10.1007/BF02386000
DOI
|
27 |
Z. Guo, P. Li, and L. Peng, Lp boundedness of commutators of Riesz transforms associated to Schrodinger operator, J. Math. Anal. Appl. 341 (2008), no. 1, 421-432. https://doi.org/10.1016/j.jmaa.2007.05.024
DOI
|
28 |
P. A. Hasto, Local-to-global results in variable exponent spaces, Math. Res. Lett. 16 (2009), no. 2, 263-278. https://doi.org/10.4310/MRL.2009.v16.n2.a5
DOI
|
29 |
G. Hu, Y. Meng, and D. Yang, Multilinear commutators of singular integrals with non doubling measures, Integral Equations Operator Theory 51 (2005), no. 2, 235-255. https://doi.org/10.1007/s00020-003-1251-y
DOI
|
30 |
P. Li and L. Peng, Lp boundedness of commutator operator associated with Schrodinger operators on Heisenberg group, Acta Math. Sci. Ser. B (Engl. Ed.) 32 (2012), no. 2, 568-578. https://doi.org/10.1016/S0252-9602(12)60039-3
DOI
|
31 |
J. Li and B. D. Wick, Weak factorizations of the Hardy space H1(ℝn) in terms of multilinear Riesz transforms, Canad. Math. Bull. 60 (2017), no. 3, 571-585. https://doi.org/10.4153/CMB-2017-033-9
DOI
|
32 |
Y. Liang, L. D. Ky, and D. Yang, Weighted endpoint estimates for commutators of Calderon-Zygmund operators, Proc. Amer. Math. Soc. 144 (2016), no. 12, 5171-5181. https://doi.org/10.1090/proc/13130
DOI
|
33 |
H. Lin, S. Wu, and D. Yang, Boundedness of certain commutators over non-homogeneous metric measure spaces, Anal. Math. Phys. 7 (2017), no. 2, 187-218. https://doi.org/10.1007/s13324-016-0136-6
DOI
|
34 |
Z. Liu and S. Lu, Two-weight weak-type norm inequalities for the commutators of fractional integrals, Integral Equations Operator Theory 48 (2004), no. 3, 397-409. https://doi.org/10.1007/s00020-002-1237-1
DOI
|
35 |
O. Kovacik and J. Rakosnik, On spaces Lp(x) and Wk,p(x), Czechoslovak Math. J. 41(116) (1991), no. 4, 592-618.
|
36 |
D. Liu, J. Tan, and J. Zhao, Multilinear commutators in variable Lebesgue spaces on stratified groups, in Analysis of pseudo-differential operators, 97-120, Trends Math, Birkhauser/Springer, Cham, 2019. https://doi.org/10.1007/978-3-030-05168-6_5
DOI
|
37 |
H. Liu and L. Tang, Compactness for higher order commutators of oscillatory singular integral operators, Internat. J. Math. 20 (2009), no. 9, 1137-1146. https://doi.org/10.1142/S0129167X09005698
DOI
|