Previous |  Up |  Next

Article

Title: Notes on commutator on the variable exponent Lebesgue spaces (English)
Author: Wang, Dinghuai
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 69
Issue: 4
Year: 2019
Pages: 1029-1037
Summary lang: English
.
Category: math
.
Summary: We obtain the factorization theorem for Hardy space via the variable exponent Lebesgue spaces. As an application, it is proved that if the commutator of Coifman, Rochberg and Weiss $[b,T]$ is bounded on the variable exponent Lebesgue spaces, then $b$ is a bounded mean oscillation (BMO) function. (English)
Keyword: bounded mean oscillation
Keyword: commutator
Keyword: Hardy space
Keyword: variable exponent Lebesgue space
MSC: 42B20
MSC: 47B07
idZBL: 07144872
idMR: MR4039617
DOI: 10.21136/CMJ.2019.0590-17
.
Date available: 2019-11-28T08:49:47Z
Last updated: 2022-01-03
Stable URL: http://hdl.handle.net/10338.dmlcz/147911
.
Reference: [1] Capone, C., Cruz-Uribe, D., Fiorenza, A.: The fractional maximal operator and fractional integrals on variable {$L^p$} spaces.Rev. Mat. Iberoam. 23 (2007), 743-770. Zbl 1213.42063, MR 2414490, 10.4171/RMI/511
Reference: [2] Chaffee, L., Cruz-Uribe, D.: Necessary conditions for the boundedness of linear and bilinear commutators on Banach function spaces.Math. Inequal. Appl. 21 (2018), 1-16. Zbl 1384.42012, MR 3716205, 10.7153/mia-2018-21-01
Reference: [3] Coifman, R. R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variables.Ann. Math. 103 (1976), 611-635. Zbl 0326.32011, MR 0412721, 10.2307/1970954
Reference: [4] Cruz-Uribe, D., Fiorenza, A., Martell, J. M., Pérez, C.: The boundedness of classical operators on variable $L^p$ spaces.Ann. Acad. Sci. Fenn., Math. 31 (2006), 239-264. Zbl 1100.42012, MR 2210118
Reference: [5] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents.Lecture Notes in Mathematics 2017 Springer, Berlin (2011). Zbl 1222.46002, MR 2790542, 10.1007/978-3-642-18363-8
Reference: [6] Janson, S.: Mean oscillation and commutators of singular integral operators.Ark. Mat. 16 (1978), 263-270. Zbl 0404.42013, MR 0524754, 10.1007/BF02386000
Reference: [7] Komori, Y.: Notes on commutators on Herz-type spaces.Arch. Math. 81 (2003), 318-326. Zbl 1053.42020, MR 2013263, 10.1007/s00013-003-0545-2
Reference: [8] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$.Czech. Math. J. 41 (1991), 592-618. Zbl 0784.46029, MR 1134951
Reference: [9] Li, J., Wick, B. D.: Weak factorizations of the Hardy space $H^1(\mathbb{R}^n)$ in terms of multilinear Riesz transforms.Canad. Math. Bull. 60 (2017), 571-585. Zbl 1372.42018, MR 3679731, 10.4153/CMB-2017-033-9
Reference: [10] Uchiyama, A.: The factorization of $H^p$ on the space of homogeneous type.Pac. J. Math. 92 (1981), 453-468. Zbl 0493.42032, MR 0618077, 10.2140/pjm.1981.92.453
.

Files

Files Size Format View
CzechMathJ_69-2019-4_10.pdf 268.3Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo