The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent

Jingshi Xu

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 1, page 13-27
  • ISSN: 0011-4642

Abstract

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The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.

How to cite

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Xu, Jingshi. "The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent." Czechoslovak Mathematical Journal 57.1 (2007): 13-27. <http://eudml.org/doc/31109>.

@article{Xu2007,
abstract = {The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.},
author = {Xu, Jingshi},
journal = {Czechoslovak Mathematical Journal},
keywords = {commutator; Calderón-Zygmund singular integral; BMO; Lebesgue space with variable exponent; maximal function; Calderón-Zygmund singular integral; BMO},
language = {eng},
number = {1},
pages = {13-27},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent},
url = {http://eudml.org/doc/31109},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Xu, Jingshi
TI - The boundedness of multilinear commutators of singular integrals on Lebesgue spaces with variable exponent
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 1
SP - 13
EP - 27
AB - The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.
LA - eng
KW - commutator; Calderón-Zygmund singular integral; BMO; Lebesgue space with variable exponent; maximal function; Calderón-Zygmund singular integral; BMO
UR - http://eudml.org/doc/31109
ER -

References

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  1. Factorization theorems for Hardy spaces in several variables, Ann. of Math. 123 (1976), 611–635. (1976) MR0412721
  2. The maximal function on variable L p   spaces, Ann. Acad. Sci. Fenn. Math. 28 (2003), 223–238. (2003) MR1976842
  3. Maximal function on generalized Lebesgue spaces L p ( · ) , Math. Inequal. Appl. 7 (2004), 245–253. (2004) MR2057643
  4. Calderón-Zygmund operators on generalized Lebesgue spaces L p ( · ) and problems related to fluid dynamics, J. Reine Angew. Math. 563 (2003), 197–220. (2003) MR2009242
  5. 10.1512/iumj.1991.40.40063, Indiana Univ. Math. J. 40 (1991), 1397–1420. (1991) MR1142721DOI10.1512/iumj.1991.40.40063
  6. 10.1007/BF02386000, Ark. Mat. 16 (1978), 263–270. (1978) Zbl0404.42013MR0524754DOI10.1007/BF02386000
  7. Commutators of singular integrals on generalized L p spaces with variable exponent, Publ. Nat. 49 (2005), 111–125. (2005) MR2140202
  8. Maximal and fractional operators in weighted L p ( x ) spaces, Revista Mat. Iberoam. 20 (2004), 493–515. (2004) MR2073129
  9. On spaces L p ( x ) and W k , p ( x ) , Czech. Math. J. 41 (1991), 592–618. (1991) MR1134951
  10. Weighted norm inequalities for the local sharp maximal function, J. Fourier Anal. Appl. 10 (2004), 465–474. (2004) Zbl1098.42013MR2093912
  11. 10.1090/S0002-9947-1972-0293384-6, Trans. Amer. Math. Soc. 165 (1972), 207–226. (1972) Zbl0236.26016MR0293384DOI10.1090/S0002-9947-1972-0293384-6
  12. Orlicz spaces and Modular spaces, Lecture Notes in Mathematics, 1034, Springer-Verlag, Berlin, 1983. (1983) Zbl0557.46020MR0724434
  13. Hardy-Littlewood maximal operator on L p ( x ) ( ℝ n ) , Math. Inequal. Appl. 7 (2004), 255–265. (2004) MR2057644
  14. 10.1006/jfan.1995.1027, J. Funct. Anal. 128 (1995), 163–185. (1995) Zbl0831.42010MR1317714DOI10.1006/jfan.1995.1027
  15. 10.1112/S0024610702003174, J. London Math. Soc. 65 (2002), 672–692. (2002) MR1895740DOI10.1112/S0024610702003174
  16. 10.1016/S0723-0869(01)80023-2, Expo. Math. 19 (2001), 369–371. (2001) MR1876258DOI10.1016/S0723-0869(01)80023-2
  17. Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics, 1748, Springer-Verlag, Berlin, 2000. (2000) MR1810360
  18. Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integral, Princeton University Press. Princeton, NJ, 1993. (1993) MR1232192

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