Notes on commutator on the variable exponent Lebesgue spaces

Dinghuai Wang

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 1029-1037
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Wang, Dinghuai. "Notes on commutator on the variable exponent Lebesgue spaces." Czechoslovak Mathematical Journal 69.4 (2019): 1029-1037. <http://eudml.org/doc/294574>.

@article{Wang2019,
abstract = {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.},
author = {Wang, Dinghuai},
journal = {Czechoslovak Mathematical Journal},
keywords = {bounded mean oscillation; commutator; Hardy space; variable exponent Lebesgue space},
language = {eng},
number = {4},
pages = {1029-1037},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Notes on commutator on the variable exponent Lebesgue spaces},
url = {http://eudml.org/doc/294574},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Wang, Dinghuai
TI - Notes on commutator on the variable exponent Lebesgue spaces
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1029
EP - 1037
AB - 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.
LA - eng
KW - bounded mean oscillation; commutator; Hardy space; variable exponent Lebesgue space
UR - http://eudml.org/doc/294574
ER -

References

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  1. Capone, C., Cruz-Uribe, D., Fiorenza, A., 10.4171/RMI/511, Rev. Mat. Iberoam. 23 (2007), 743-770. (2007) Zbl1213.42063MR2414490DOI10.4171/RMI/511
  2. Chaffee, L., Cruz-Uribe, D., 10.7153/mia-2018-21-01, Math. Inequal. Appl. 21 (2018), 1-16. (2018) Zbl1384.42012MR3716205DOI10.7153/mia-2018-21-01
  3. Coifman, R. R., Rochberg, R., Weiss, G., 10.2307/1970954, Ann. Math. 103 (1976), 611-635. (1976) Zbl0326.32011MR0412721DOI10.2307/1970954
  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. (2006) Zbl1100.42012MR2210118
  5. Diening, L., Harjulehto, P., Hästö, P., Růžička, M., 10.1007/978-3-642-18363-8, Lecture Notes in Mathematics 2017 Springer, Berlin (2011). (2011) Zbl1222.46002MR2790542DOI10.1007/978-3-642-18363-8
  6. Janson, S., 10.1007/BF02386000, Ark. Mat. 16 (1978), 263-270. (1978) Zbl0404.42013MR0524754DOI10.1007/BF02386000
  7. Komori, Y., 10.1007/s00013-003-0545-2, Arch. Math. 81 (2003), 318-326. (2003) Zbl1053.42020MR2013263DOI10.1007/s00013-003-0545-2
  8. Kováčik, O., Rákosník, J., On spaces L p ( x ) and W k , p ( x ) , Czech. Math. J. 41 (1991), 592-618. (1991) Zbl0784.46029MR1134951
  9. Li, J., Wick, B. D., 10.4153/CMB-2017-033-9, Canad. Math. Bull. 60 (2017), 571-585. (2017) Zbl1372.42018MR3679731DOI10.4153/CMB-2017-033-9
  10. Uchiyama, A., 10.2140/pjm.1981.92.453, Pac. J. Math. 92 (1981), 453-468. (1981) Zbl0493.42032MR0618077DOI10.2140/pjm.1981.92.453

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