In this paper, the boundedness properties for some Toeplitz type operators associated to the Riesz potential and general integral operators from Lebesgue spaces to Orlicz spaces are proved. The general integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.
@article{bwmeta1.element.doi-10_1515_math-2015-0065, author = {Dazhao Chen}, title = {Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space}, journal = {Open Mathematics}, volume = {13}, year = {2015}, zbl = {06484392}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0065} }
Dazhao Chen. Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0065/
[1] Chang D.C., Li J.F., Xiao J., Weighted scale estimates for Calderón-Zygmund type operators, Contemporary Mathematics, 2007, 446, 61-70. | Zbl 1188.42004
[2] Chanillo S., A note on commutators, Indiana Univ. Math. J., 1982, 31, 7-16. [Crossref] | Zbl 0523.42015
[3] Coifman R., Rochberg R., Weiss G., Factorization theorems for Hardy spaces in several variables, Ann. of Math., 1976, 103, 611-635. | Zbl 0326.32011
[4] Garcia-Cuerva J., Rubio de Francia J. L., Weighted norm inequalities and related topics, North-Holland Math., 1985, Amsterdam, 116. | Zbl 0578.46046
[5] Janson S., Mean oscillation and commutators of singular integral operators, Ark. for Mat., 1978, 16, 263-270. | Zbl 0404.42013
[6] Janson S., Peetre J., Paracommutators boundedness and Schatten-von Neumann properties, Tran. Amer. Math. Soc.,1988, 305, 467-504. | Zbl 0644.47046
[7] Janson S., Peetre J., Higher order commutators of singular integral operators, Interpolation spaces and allied topics in analysis, Lecture Notes in Math., 1984, Springer, Berlin, 1070, 125-142.
[8] Lin Y., Sharp maximal function estimates for Calderón-Zygmund type operators and commutators, Acta Math. Scientia, 2011, 31(A), 206-215. | Zbl 1240.42051
[9] Liu L.Z., Continuity for commutators of Littlewood-Paley operator on certain Hardy spaces, J. Korean Math. Soc., 2003, 40, 41-60. [Crossref] | Zbl 1026.42021
[10] Liu L.Z., The continuity of commutators on Triebel-Lizorkin spaces, Integral Equations and Operator Theory, 2004, 49, 65-76.
[11] Liu L.Z., Sharp and weighted inequalities for multilinear integral operators, Revista de la Real Academia de Ciencias Exactas, Serie A: Matematicas, 2007, 101, 99-111. | Zbl 1202.42041
[12] Liu L.Z., Weighted boundedness for multilinear Littlewood-Paley and Marcinkiewicz operators on Morrey spaces, J. Cont. Math. Anal., 2011, 46, 49-66. [WoS]
[13] Liu L.Z., Sharp maximal function estimates and boundedness for commutators associated with general integral operator, Filomat, 2011, 25, 137-151. | Zbl 1265.42038
[14] Liu L.Z., Multilinear singular integral operators on Triebel-Lizorkin and Lebesgue spaces, Bull. of the Malaysian Math. Sci. Soc., 2012, 35, 1075-1086. | Zbl 1250.42047
[15] Lu S.Z., Four lectures on real Hp spaces, World Scienti?c, River Edge, NI, 1995.
[16] Paluszynski M., Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss, Indiana Univ. Math. J., 1995, 44, 1-17. | Zbl 0838.42006
[17] Pérez C., Pradolini G., Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J., 2001, 49, 23-37. | Zbl 1010.42007
[18] Pérez C., Trujillo-Gonzalez R., Sharp weighted estimates for multilinear commutators, J. London Math. Soc., 2002, 65, 672-692. | Zbl 1012.42008
[19] Stein E.M., Harmonic analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993. | Zbl 0821.42001
[20] Torchinsky A., Real variable methods in harmonic analysis, Pure and Applied Math., 123, Academic Press, New York, 1986. | Zbl 0621.42001
[21] Torchinsky A., WangS., A note on the Marcinkiewicz integral, Colloq. Math., 1990, 60/61, 235-24. | Zbl 0731.42019
[22] Wu B.S., Liu L.Z., A sharp estimate for multilinear Bochner-Riesz operator, Studia Sci. Math. Hungarica, 2005, 42, 47-59. | Zbl 1109.42003