Boundedness for multilinear Marcinkiewicz integral operators on Hardy and Herz–Hardy spaces
Abstract
The purpose of this paper is to establish the boundedness for some multilinear operators generated by Marcinkiewicz integral operators and Lipschitz functions on Hardy and Herz-Hardy spaces.
Keywords
multilinear operators; Marcinkiewicz integral operator; Lipschitz space; Hardy space; Herz-Hardy space
References
2. Cohen J., A sharp estimate for a multilinear singular integral on R^n, Indiana Univ. Math. J., 30 (1981), 693-702.
3. Cohen J., Gosselin J., On multilinear singular integral operators on R^n, Studia Math., 72 (1982), 199-223.
4. Cohen J., Gosselin J., A BMO estimate for multilinear singular integral operators, Illinois J. Math., 30 (1986), 445-465.
5. Ding Y., Lu Z.S., Weighted boundedness for a class rough multilinear operators, Acta Math. Sinica, 17 (2001), 517-526.
6. Garcia-Cuerva J., Herrero M.J.L., A theory of Hardy spaces associated to Herz spaces, Proc. London Math. Soc., 69 (1994), 605-628.
7. Garcia-Cuerva J., Rubio de Francia J.L., Weighted norm inequalities and related topics, North-Holland Math., 16 (1985), Amsterdam.
8. Janson S., Mean oscillation and commutators of singular integral operators, Ark. Math., 16 (1978), 263-270.
9. Liu L.Z., Boundedness for multilinear Marcinkiewicz operators on certain Hardy Spaces, Inter. J. of Math. and Math. Sci., 2 (2003), 87-96.
10. Liu L.Z., Endpoint estimates for multilinear Marcinkiewicz integral operators, East J. on Approx., 9 (2003), 339-350.
11. Liu L.Z., Triebel-Lizorkin spaces estimates for multilinear operators of sublinear operators, Proc. Indian Acad. Sci. (Math. Sci), 113 (2003), 379-393.
12. Lu L.Z., Wu Q., Yang D.C., Boundedness of commutators on Hardy type spaces, Sci. in China (ser. A), 45 (2002), 984-997.
13. L u S.Z., Yang D.C., The decomposition of the weighted Herz spaces and its applications, Sci. in China (ser. A), 38 (1995), 147-158.
14. Lu S.Z., Yang D.C., The weighted Herz type Hardy spaces and its applications, Sci. in China (ser. A), 38 (1995), 662-673.
15. Paluszynski M., Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 44 (1995), 1-17.
16. Torchinsky A., Wang S., A note on the Marcinkiewicz integral, Colloq. Math., 60/61 (1990), 235-243.
College of Mathematics, Changsha Univeristy of Science and Technology, China China
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