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WEIGHTED ESTIMATES FOR MULTIVARIATE HAUSDORFF OPERATORS

WEIGHTED ESTIMATES FOR MULTIVARIATE HAUSDORFF OPERATORS
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摘要 In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on LP spaces with power weights, which is based on the boundedness of multivariate Hausdorff operators on Herz spaces, and are bounded on weighted LP spaces with the weights satisfying the homogeneity of degree zero. In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on LP spaces with power weights, which is based on the boundedness of multivariate Hausdorff operators on Herz spaces, and are bounded on weighted LP spaces with the weights satisfying the homogeneity of degree zero.
作者 Yanling Sun Yinsheng Jiang
机构地区 Xinjiang University
出处 《Analysis in Theory and Applications》 2012年第3期278-285,共8页 分析理论与应用（英文刊）
基金 Supported by NNSF of China (10861010,11161044)
关键词 multivariate Hausdorff operator weighted Lp space Herz space multivariate Hausdorff operator, weighted Lp space, Herz space
分类号 O177.6 [理学—基础数学] O175.5 [理学—基础数学]
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参考文献7

  • 1Hardy, G. H., Divergent Series, Clarendon Press, Oxford, 1949.
  • 2Brown,G. and M6ricz, F., The Hausdorff and the Quasi Hausdorff Operators on the Spaces/P, 1 < p < oo, Math.Inequal.Appl., 3(2000), 105-115.
  • 3Brown,G. and M6ricz, F., Multivariate Hausdorff Operators on the Spaces LP(Rn), J.Math.Anal.Appl., 271 (2002), 443-454.
  • 4Kamke, E., Das Lebesgue-Stieltjes Integral, Teubner, Leipzig, 1956.
  • 5Sas, S., Theory of the Integral, 2nd rev.ed., Dover, New York, 1964.
  • 6Moricz, F., Multivariate Hausdorff Operators on the Spaces H1 (Rn) and BMO(Rn), Analysis Mathematica, 31(2005), 31-41.
  • 7Lu, S.Z., Yang D.C. and I-Iu G.E., Herz Type Spaces and Their Applications, Science Press, Beijing, 2008.
Analysis in Theory and Applications
2012年 第3期

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