Title:
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Notes on commutator on the variable exponent Lebesgue spaces (English) |
Author:
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Wang, Dinghuai |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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69 |
Issue:
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4 |
Year:
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2019 |
Pages:
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1029-1037 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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:
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bounded mean oscillation |
Keyword:
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commutator |
Keyword:
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Hardy space |
Keyword:
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variable exponent Lebesgue space |
MSC:
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42B20 |
MSC:
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47B07 |
idZBL:
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07144872 |
idMR:
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MR4039617 |
DOI:
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10.21136/CMJ.2019.0590-17 |
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Date available:
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2019-11-28T08:49:47Z |
Last updated:
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2022-01-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/147911 |
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Reference:
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[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:
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[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 |
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