Abstract
In this paper, the authors study the boundedness of the operator [μΩ,b], the commutator generated by a functionb∈Lip β (ℝn)(0<β≤1) and the Marcinkiewicz integrals \gm\gW, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈Lipα(S n−1)(0<≤1).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Stein, E. M., On the Function of Littlewood-Paley, Lusin and Marcinkiewicz, Trans. Amer. Math. Soc., 88(1958) 430–466.
Benedek, A., Calderón, A. and Panzone, R., Convolution Operators on Banach Space Valued Functions, Proc. Nat. Acad. Sci. USA, 48(1962), 356–365.
Ding, Y., Fan, D. and Pan, Y., Weighted Boundedness for a Class of Rough Marcinkiewicz Integrals, Indiana Univ. Math. J., 48(1999), 1037–1055.
Ding, Y., Fan, D. and Pan, Y.,L p-Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernel, Acta Math. Sinica (English Series), 16(2000), 593–600.
Colzani, L., Taibleson, M.H. and Weiss, G., Maximal Estimates for Cesaro and Riesz Means on Sphere, Indiana Univ. Math. J., 33(1984), 873–889.
Chen, J.C., Xu, H. and Ying, Y.M., A Note on Marcinkiewicz Integrals withH 1 Kernel, to Appear in Acta. Math. Scientia.
Torchinsky, A. and Wang, S., A Note on the Marcinkiewicz Integral, Colloquium Math, 60/61 (1990), 235–243.
Ding, Y., Lu, S.Z. and Yabuta, K., On Commutators of Marcinkiewicz Integrals with Rough Kernel, Preprint.
Wang, Y., A Note Commutator of Marcinkiewicz Integral, Preprint.
Stein, E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, N. J., 1993.
Lu, S.Z., Four Lectures on RealH p Spaces, World Scientific Publishing Co. Pte. Ltd., 1995.
Li, X.W. and Yang, D.C., Boundedness of Some Sublinear Operators on Herz Spaces, Illinois J. Math., 40(1996), 484–501.
Lu, S.Z. and Yang, D.C., The Weighted Herz-Type Hardy Space and Its Applications, Sci. in China (Ser. A), 38(1995), 662–673.
Hu, G.E., Lu, S.Z. and Yang, D.C., The Weak Herz Spaces, J. of Beijing Norm. Univ. (Nat. Sci.), 33(1997), 27–34.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National 973 Project (G.19990751) and the SEDF (20010027002).
Rights and permissions
About this article
Cite this article
Shanzhen, L., Lifang, X. Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces. Anal. Theory Appl. 20, 215–230 (2004). https://doi.org/10.1007/BF02835290
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02835290