Weighted boundedness of a multilinear operator associated to a singular integral operator with general kernels

详细信息    查看全文

• 作者：Qiufen Feng (14)
  
  14. Changsha Commerce and Tourism College ; Changsha ; 410116 ; P.R. China
  
• 关键词：multilinear operator ; singular integral operator ; sharp maximal function ; weighted BMO ; weighted Lipschitz function
• 刊名：Journal of Inequalities and Applications
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：224 KB
• 参考文献：1. Garcia-Cuerva, J, Rubio de Francia, JL (1985) North-Holland Mathematics Studies 16. Weighted Norm Inequalities and Related Topics. North-Holland, Amsterdam
  2. Stein, EM (1993) Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals. Princeton University Press, Princeton
  3. Torchinsky, A (1986) Pure and Applied Math. 123. Real Variable Methods in Harmonic Analysis. Academic Press, New York
  4. Coifman, RR, Rochberg, R, Weiss, G (1976) Factorization theorems for Hardy spaces in several variables. Ann. Math 103: pp. 611-635 CrossRef
  5. P茅rez, C (1995) Endpoint estimate for commutators of singular integral operators. J. Funct. Anal 128: pp. 163-185 CrossRef
  6. P茅rez, C, Trujillo-Gonzalez, R (2002) Sharp weighted estimates for multilinear commutators. J. Lond. Math. Soc 65: pp. 672-692 CrossRef
  7. Chanillo, S (1982) A note on commutators. Indiana Univ. Math. J 31: pp. 7-16 CrossRef
  8. Lin, Y (2011) Sharp maximal function estimates for Calder贸n-Zygmund type operators and commutators. Acta Math. Sci., Ser. A 31: pp. 206-215
  9. Paluszynski, M (1995) Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J 44: pp. 1-17 CrossRef
  10. Bloom, S (1985) A commutator theorem and weighted BMO. Trans. Am. Math. Soc 292: pp. 103-122 CrossRef
  11. Hu, B, Gu, J (2008) Necessary and sufficient conditions for boundedness of some commutators with weighted Lipschitz spaces. J. Math. Anal. Appl 340: pp. 598-605 CrossRef
  12. Chang, DC, Li, JF, Xiao, J (2007) Weighted scale estimates for Calder贸n-Zygmund type operators. Contemp. Math 446: pp. 61-70 CrossRef
  13. Liu, LZ (2011) Sharp maximal function estimates and boundedness for commutators associated with general integral operator. Filomat 25: pp. 137-151 CrossRef
  14. Garcia-Cuerva, J (1979) Weighted spaces. Diss. Math 162: pp. 1-63
  15. Peetre, J (1966) On convolution operators leaving -spaces invariant. Ann. Mat. Pura Appl 72: pp. 295-304 CrossRef
  16. Peetre, J (1969) On the theory of -spaces. J. Funct. Anal 4: pp. 71-87 CrossRef
  17. Di Fazio, G, Ragusa, MA (1991) Commutators and Morrey spaces. Boll. Unione Mat. Ital., A 5: pp. 323-332
  18. Di Fazio, G, Ragusa, MA (1993) Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients. J. Funct. Anal 112: pp. 241-256 CrossRef
  19. Liu, LZ (2005) Interior estimates in Morrey spaces for solutions of elliptic equations and weighted boundedness for commutators of singular integral operators. Acta Math. Sci., Ser. B 25: pp. 89-94
  20. Mizuhara, T (1990) Boundedness of some classical operators on generalized Morrey spaces. Harmonic Analysis: Proceedings of a Conference Held in Sendai. pp. 183-189
  21. Cohen, J, Gosselin, J (1982) On multilinear singular integral operators on. Stud. Math 72: pp. 199-223
  22. Cohen, J, Gosselin, J (1986) A BMO estimate for multilinear singular integral operators. Ill. J. Math 30: pp. 445-465
  23. Ding, Y, Lu, SZ (2001) Weighted boundedness for a class rough multilinear operators. Acta Math. Sin 17: pp. 517-526 CrossRef
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

In this paper, we establish the weighted sharp maximal function inequalities for a multilinear operator associated to a singular integral operator with general kernels. As an application, we obtain the boundedness of the operator on weighted Lebesgue and Morrey spaces. MSC: 42B20, 42B25.