Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space
Open Mathematics (2015)
- Volume: 13, Issue: 1, page 413-426
- ISSN: 2391-5455
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topDazhao Chen. "Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space." Open Mathematics 13.1 (2015): 413-426. <http://eudml.org/doc/275871>.
@article{DazhaoChen2015,
abstract = {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.},
author = {Dazhao Chen},
journal = {Open Mathematics},
keywords = {Toeplitz type operator; Singular integral operator; Orlicz space; BMO space; Lipschitz function; singular integral operator; fractional integral operator; sharp maximal function; BMO; Morrey space},
language = {eng},
number = {1},
pages = {413-426},
title = {Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space},
url = {http://eudml.org/doc/275871},
volume = {13},
year = {2015},
}
TY - JOUR
AU - Dazhao Chen
TI - Boundedness of Toeplitz type operators associated to Riesz potential operator with general kernel on Orlicz space
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 413
EP - 426
AB - 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.
LA - eng
KW - Toeplitz type operator; Singular integral operator; Orlicz space; BMO space; Lipschitz function; singular integral operator; fractional integral operator; sharp maximal function; BMO; Morrey space
UR - http://eudml.org/doc/275871
ER -
References
top- [1] Chang D.C., Li J.F., Xiao J., Weighted scale estimates for Calderón-Zygmund type operators, Contemporary Mathematics, 2007, 446, 61-70. Zbl1188.42004
- [2] Chanillo S., A note on commutators, Indiana Univ. Math. J., 1982, 31, 7-16. [Crossref] Zbl0523.42015
- [3] Coifman R., Rochberg R., Weiss G., Factorization theorems for Hardy spaces in several variables, Ann. of Math., 1976, 103, 611-635. Zbl0326.32011
- [4] Garcia-Cuerva J., Rubio de Francia J. L., Weighted norm inequalities and related topics, North-Holland Math., 1985, Amsterdam, 116. Zbl0578.46046
- [5] Janson S., Mean oscillation and commutators of singular integral operators, Ark. for Mat., 1978, 16, 263-270. Zbl0404.42013
- [6] Janson S., Peetre J., Paracommutators boundedness and Schatten-von Neumann properties, Tran. Amer. Math. Soc.,1988, 305, 467-504. Zbl0644.47046
- [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. Zbl1240.42051
- [9] Liu L.Z., Continuity for commutators of Littlewood-Paley operator on certain Hardy spaces, J. Korean Math. Soc., 2003, 40, 41-60. [Crossref] Zbl1026.42021
- [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. Zbl1202.42041
- [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. Zbl1265.42038
- [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. Zbl1250.42047
- [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. Zbl0838.42006
- [17] Pérez C., Pradolini G., Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J., 2001, 49, 23-37. Zbl1010.42007
- [18] Pérez C., Trujillo-Gonzalez R., Sharp weighted estimates for multilinear commutators, J. London Math. Soc., 2002, 65, 672-692. Zbl1012.42008
- [19] Stein E.M., Harmonic analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993. Zbl0821.42001
- [20] Torchinsky A., Real variable methods in harmonic analysis, Pure and Applied Math., 123, Academic Press, New York, 1986. Zbl0621.42001
- [21] Torchinsky A., WangS., A note on the Marcinkiewicz integral, Colloq. Math., 1990, 60/61, 235-24. Zbl0731.42019
- [22] Wu B.S., Liu L.Z., A sharp estimate for multilinear Bochner-Riesz operator, Studia Sci. Math. Hungarica, 2005, 42, 47-59. Zbl1109.42003
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