Abstract
The boundedness of maximal Bochner-Riesz operator Bδ* and that of maximal commutator Bbδ,* generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space are established.
Similar content being viewed by others
References
Calderón, A. P., Commutators of Singular Integral Operators, Proc. Nat. Acad. Sci. USA, 53(1965), 1092–1099.
Calderón, A. P., Cauchy Integrals on Lipschitz Curves and Related Operators, Proc. Nat. Acad. Sci. USA, 74(4)(1977), 1324–1327.
Coifman, R., Rochberg, R. and Weiss, G., Fractorization Theorems for Hardy Spaces in Several Variables, Ann. of Math. J., 103(1976), 611–635.
Hu, G. E. and Lu, S. Z., The Commutator of the Bochner-Riesz Operator, Tohoku Math. J., 48(1996), 259–266.
Hu, G. E. and Lu, S. Z., The Maximal Operator Associated with the Commutator of the Bochner-Riesz Operator, Beijing Math. J., 21(1996), 96–106.
Lu, S. Z. and Yang, D. C., The Continuity of Commutators on Herz-Type Spaces, Michigan Math. J., 44(1997), 255–281.
Liu, L. Z. and Lu, S. Z., Weighted Weak Type Inequalities for Maximal Commutators of Bochner-Riesz Operator, Hokkaido Math. J., 32(2003), 85–96.
Liu, L. Z., The Continuity of Commutators on Triebel-Lizorkin Spaces, Integral Equations and Operator Theory, 49(2004), 65–75.
Lu, S. Z., Four Lectures on Real H p Spaces, World Scientific Publishing, River Edge, N. J., 1995.
Chiarenza, F. and Frasca, M., Morrey Space and Hardy-Littlewood Maximal Function, Rend. Mat., 7(1987), 273–279.
Lin, Y., Strongly Singular Calderón-Zygmund Operator and Commutator on Morrey Type Spaces, Acta Math. Sinica (English Ser.), 23(11)(2007), 2097–2110.
Liu, L. Z., Interior Estimates in Morrey Spaces for Solutions of Elliptic Equations and Weighted Boundedness for Commutators of Singular Integral Operators, Acta Math. Scientia., 25(2005), 89–94.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by NSFC(10571014),NSFC(10571156), the growth foundation of JXNU (1983) and the doctor foundation of JXNU.
Rights and permissions
About this article
Cite this article
Liu, Y., Chen, D. The boundedness of maximal Bochner-Riesz operator and maximal commutator on Morrey type spaces. Anal. Theory Appl. 24, 321–329 (2008). https://doi.org/10.1007/s10496-008-0321-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10496-008-0321-z