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Mk-type Estimates for Multilinear Commutator of Multiplier Operator
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In this paper, we prove the Mk-type inequality for the multilinear commutator related to the multiplier operator. By using the Mk-type inequality, we obtain the weightedLp-norm inequality and the weighted estimates on the generalized Morrey spaces for the multilinear commutator.
Keywords
Multilinear Commutator, Multiplier Operator, BMO, Morrey Spaces
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- F. Chiarenza and M. Frasca, Moreey spaces and Hardy-Littlewood maximal function, Rend. Mat., 7(1987), 273-279.
- R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math., 103(1976), 611-635.
- G. Di FaZio and M. A. Ragusa, Commutators and Morrey spaces, Boll. Un. Mat. Ital., (7)5-A(1991), 323-332.
- J. Garcia-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Math. 116, Amsterdam, 1985.
- D. S. Kurtz and R. L. Wheeden, Results on weighted norm inequalities for multiplies, Trans. Amer. Math. Soc., 255(1979), 343-362.
- D. S. Kurtz, Sharp function estimates for fractional integrals and related operators, J. Austral. Math. Soc., 49(A)(1990), 129-137.
- S. Z. Lu, Four lectures on real Hp spaces, World Scientific, River Edge, NJ, 1995.
- S. Z. Lu and D. C. Yang, Multiplier theorem for Herz type Hardy spaces, Proc. Amer. Math. Soc., 126(1998), 3337-3346.
- B. Muckenhoupt, R. L. Wheeden and W. S. Young, Sufficient conditions for Lp multipliers with general weights, Trans. Amer. Math. Soc., 300(1987), 463-502.
- J. Peetre, On convolution operators leaving Lp,λ-spaces invariant, Ann. Mat. Pura. Appl., 72(1966), 295-304.
- J. Peetre, On the theory of Lp,λ-spaces, J. Func. Anal., 4(1969), 71-87.
- C. Perez, Endpoint estimate for commutators of singular integral operators, J. Func. Anal., 128(1995), 163-185.
- C. Perez and G. Pradolini, Sharp weighted endpoint estimates for commutators of singular integral operators, Michigan Math. J., 49(2001), 23-37.
- C. Perez and R. Trujillo-Gonzalez, Sharp Weighted estimates for multilinear commutators, J. London Math. Soc., 65(2002), 672-692.
- E. M. Stein, Singular integrals and differentiability properties of function, Princeton Univ. Press, Princeton NJ, 1970.
- E. M. Stein, Harmonic analysis: real variable methods, orthogonality and oscillatory integrals, Princeton Univ. Press, Princeton NJ, 1993.
- P. Zhang and J.C. Chen, The (Lp, Ḟpβ,∞)-boundedness of commutators of multiplies, Acta Math. Sinica, 21(2005), 765-772.
- P. Zhang and J. C. Chen, Boundedness properties for commutators of multiplies, Acta Math. Sinica (Chinese Series), 49(2006), 1387-1396.
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