Endpoint Estimates for Multilinear Fractional Singular Integral Operators on Some Hardy Spaces
Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 735-752.

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

In this paper, the endpoint estimates for some multilinear operators related to certain fractional singular integral operators on some Hardy and Herz-type Hardy spaces are obtained.
Keywords: multilinear operator, fractional singular integral operators, BMO space, Hardy space, Herz space, Herz-type Hardy space.
@article{MZM_2010_88_5_a8,
     author = {Liu Lanzhe},
     title = {Endpoint {Estimates} for {Multilinear} {Fractional} {Singular} {Integral} {Operators} on {Some} {Hardy} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {735--752},
     publisher = {mathdoc},
     volume = {88},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a8/}
}
TY  - JOUR
AU  - Liu Lanzhe
TI  - Endpoint Estimates for Multilinear Fractional Singular Integral Operators on Some Hardy Spaces
JO  - Matematičeskie zametki
PY  - 2010
SP  - 735
EP  - 752
VL  - 88
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a8/
LA  - ru
ID  - MZM_2010_88_5_a8
ER  - 
%0 Journal Article
%A Liu Lanzhe
%T Endpoint Estimates for Multilinear Fractional Singular Integral Operators on Some Hardy Spaces
%J Matematičeskie zametki
%D 2010
%P 735-752
%V 88
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a8/
%G ru
%F MZM_2010_88_5_a8
Liu Lanzhe. Endpoint Estimates for Multilinear Fractional Singular Integral Operators on Some Hardy Spaces. Matematičeskie zametki, Tome 88 (2010) no. 5, pp. 735-752. http://geodesic.mathdoc.fr/item/MZM_2010_88_5_a8/

[1] R. R. Coifman, R. Rochberg, G. Weiss, “Factorization theorems for Hardy spaces in several variables”, Ann. of Math. (2), 103:3 (1976), 611–635 | DOI | MR | Zbl

[2] S. Chanillo, “A note on commutators”, Indiana Univ. Math. J., 31:1 (1982), 7–16 | DOI | MR | Zbl

[3] E. Harboure, C. Segovia, J. L. Torrea, “Boundedness of commutators of fractional and singular integrals for the extreme values of $p$”, Illinois J. Math., 41:4 (1997), 676–700 | MR | Zbl

[4] J. García-Cuerva, “Hardy spaces and Beurling algebras”, J. London Math. Soc. (2), 39:3 (1989), 499–513 | DOI | MR | Zbl

[5] J. García-Cuerva, M.-J. L. Herrero, “A theory of Hardy spaces associated to the Herz spaces”, Proc. London Math. Soc. (3), 69:3 (1994), 605–628 | DOI | MR | Zbl

[6] Lu Shanzhen, Yang Dachun, “The decomposition of weighted Herz space on $\mathbf R^n$ and its applications”, Sci. China Ser. A, 38:2 (1995), 147–158 | MR | Zbl

[7] Lu Shanzhen, Yang Dachun, “The weighted Herz-type Hardy space and its applications”, Sci. China Ser. A, 38:6 (1995), 662–673 | MR | Zbl

[8] J. García-Cuerva, J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math. Stud., 116, Notas de Matemática, 104, North-Holland Publ., Amsterdam, 1985 | MR | Zbl

[9] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser., 43, Monographs in Harmonic Analysis, III, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[10] J. Cohen, “A sharp estimate for a multilinear singular integral in $\mathbb R^n$”, Indiana Univ. Math. J., 30:5 (1981), 693–702 | MR | Zbl

[11] J. Cohen, J. Gosselin, “On multilinear singular integral operators on $\mathbb R^n$”, Studia Math., 72:3 (1982), 199–223 | MR

[12] J. Cohen, J. Gosselin, “A BMO estimate for multilinear singular integrals”, Illinois J. Math., 30:3 (1986), 445–465 | MR | Zbl

[13] Y. Meyer, R. Coifman, Wavelets, Calderón–Zygmund and multilinear operators, Cambridge Stud. Adv. Math., 48, Cambridge Univ. Press, Cambridge, 1997 | MR | Zbl

[14] Ding Yong, Lu Shan Zhen, “Weighted boundedness for a class of rough multilinear operators”, Acta Math. Sin. (Engl. Ser.), 17:3 (2001), 517–526 | DOI | MR | Zbl

[15] Chen Wengu, Hu Guoen, “Weak type ($H^1$, $L^1$) estimate for a multilinear singular integral operator”, Adv. Math. (China), 30:1 (2001), 63–69 | MR | Zbl