Boundedness of Hyper-Singular Parametric Marcinkiewicz Integrals with Variable Kernels

DOI: 10.4236/am.2013.411A3005   PDF   HTML   XML   2,283 Downloads   3,471 Views  

Abstract

In this article, we consider the boundedness of  on Hardy type space  . Where   

  
 

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Q. Fang and X. Shi, "Boundedness of Hyper-Singular Parametric Marcinkiewicz Integrals with Variable Kernels," Applied Mathematics, Vol. 4 No. 11C, 2013, pp. 28-34. doi: 10.4236/am.2013.411A3005.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] X. X. Tao, X. Yu and S. Y. Zhang, “Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels,” Journal of Inequalities and Applications, Vol. 2008, 2008, pp. 1-17.
http://dx.doi.org/10.1155/2008/835938
[2] Y. Ding and R. Li, “An Estimate of Bessel Function and Its Application,” Science in China, Series A, Vol. 51, 2008, pp. 897-906.
http://dx.doi.org/10.1007/s11425-008-0004-4
[3] M. Paluszynski, “Characterization of the Besov Spaces via the Commutator Operator of Coifman, Rochberg and Weiss,” Indiana University Mathematics Journal, Vol. 44, 1995, pp. 1-18.
http://dx.doi.org/10.1512/iumj.1995.44.1976
[4] S. Z. Lu and L. F. Xu, “Boundedness of Some Marcinkie wicz Integral Operators Related to Higher Order Commu tators on Hardy Spaces,” Acta Mathematica Sinica, Eng lish Series, Vol. 22, 2006, pp. 105-114.
http://dx.doi.org/10.1007/s10114-005-0545-1
[5] C. Pérez and R. Trujillo-gonzález, “Sharp Weighted Es timates for Multilinear Commutators,” Journal of the London Mathematical Society, Vol. 65, 2002, pp. 672-692.
http://dx.doi.org/10.1112/S0024610702003174
[6] Y. Ding, C. C. Lin and Y. C. Lin, “Erratum: On Marcin kiewicz Integral with Variable Kernels,” Indiana Univer sity Mathematics Journal, Vol. 56, 2007, pp. 991-994.
http://dx.doi.org/10.1512/iumj.2007.56.3176
[7] B. Muckenhoupt, and R. L. Wheeden, “Weighted Norm Inequalities for Singular and Fractional Integrals,” Tran sactions of the American Mathematical Society, Vol. 161, 1971, pp. 249-261.
http://dx.doi.org/10.1090/S0002-9947-1971-0285938-7

  
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