Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces
Lobachevskii journal of mathematics, Tome 22 (2006), pp. 7-18.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the $(H^p_{\vec{b}},L^p)$ and $(H\dot{K}^{\alpha,p}_{q,\vec{b}},\dot{K}_q^{\alpha,p})$ type boundedness for the multilinear commutator associated with the Littlewood–Paley operator are obtained.
Keywords: Littlewood–Paley operator, Multilinear commutator, BMO, Hardy space, Herz–Hardy space.
@article{LJM_2006_22_a1,
     author = {Ch. Wu and L. Liu},
     title = {Boundedness for multilinear commutator of {Littlewood--Paley} operator on {Hardy} and {Herz--Hardy} spaces},
     journal = {Lobachevskii journal of mathematics},
     pages = {7--18},
     publisher = {mathdoc},
     volume = {22},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2006_22_a1/}
}
TY  - JOUR
AU  - Ch. Wu
AU  - L. Liu
TI  - Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces
JO  - Lobachevskii journal of mathematics
PY  - 2006
SP  - 7
EP  - 18
VL  - 22
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2006_22_a1/
LA  - en
ID  - LJM_2006_22_a1
ER  - 
%0 Journal Article
%A Ch. Wu
%A L. Liu
%T Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces
%J Lobachevskii journal of mathematics
%D 2006
%P 7-18
%V 22
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2006_22_a1/
%G en
%F LJM_2006_22_a1
Ch. Wu; L. Liu. Boundedness for multilinear commutator of Littlewood--Paley operator on Hardy and Herz--Hardy spaces. Lobachevskii journal of mathematics, Tome 22 (2006), pp. 7-18. http://geodesic.mathdoc.fr/item/LJM_2006_22_a1/

[1] J. Alvarez, “Continuity properties for linear commutators of Calderón-Zygmund operators”, Collect. Math., 49 (1998), 17–31 | MR | Zbl

[2] R. Coifman, R. Rocherg and G. Weiss, “Factorization theorem for Hardy space in several variables”, Ann. of Math., 103 (1976), 611–635 | DOI | MR | Zbl

[3] J. Garcia-Cuerva and M. L. Herrero, “A Theory of Hardy spaces associated to Herz Spaces”, Proc. London Math. Soc., 69 (1994), 605–628 | DOI | MR | Zbl

[4] L. Z. Liu, “Weighted weak type $(H^1,L^1)$ estimates for commutators of Littlewood–Paley operators”, Indian J. of Math., 45:1 (2003), 71–78 | MR | Zbl

[5] L. Z. Liu, “Weighted Block–Hardy spaces estimates for commutators of Littlewood–Paley operators”, Southeast Asian Bull. of Math., 27 (2004), 833–838 | MR | Zbl

[6] L. Z. Liu, “Weighted weak type estimates for commutators of Littlewood–Paley operator”, Japanese J. of Math., 29:1 (2003), 1–13 | MR

[7] L. Z. Liu, S. Z. Lu and J. S. Xu, “Boundedness for commutators of Littlewood–Paley operators”, Adv. in Math. (China), 32 (2003), 473–480 | MR

[8] S. Z. Lu and D. C. Yang, “The local versions of $H^p(R^n)$ spaces at the origin”, Studia. Math., 116 (1995), 147–158 | MR

[9] S. Z. Lu and D. C. Yang, “The decomposition of the weighted Herz spaces and its applications”, Sci. in China (ser. A), 38 (1995), 147–158 | MR | Zbl

[10] S. Z. Lu and D. C. Yang, “The weighted Herz type Hardy spaces and its applications”, Sci. in China (ser. A), 38 (1995), 662–673 | MR | Zbl

[11] S. Z. Lu and D. C. Yang, “The continuity of commutators on Herz-type space”, Michigan Math. J., 44 (1997), 255–281 | DOI | MR | Zbl

[12] C. Pérez, “Endpoint estimate for commutators of singular integral operators”, J. Func. Anal., 128 (1995), 163–185 | DOI | MR | Zbl

[13] C. Pérez and R. Trujillo-Gonzalez, “Sharp weighted estimates for multilinear commutators”, J. London Math. Soc., 65 (2002), 672–692 | DOI | MR | Zbl

[14] E. M. Stein, Harmonic Analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[15] A. Torchinsky, The real variable methods in harmonic analysis, Pure and Applied Math., 123, Academic Press, New York, 1986 | MR | Zbl