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关于Herz型空间中加权Hard-Littlewood平均的一个注记(英文) 被引量:3

A Remark on Weighted Hardy-Littlewood Averages on Herz-type Spaces
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摘要 本文给出了加权Hardy-Littlewood平均在Herz型空间中关于权有界的充分必要条件. In this note, the authors established a sufficient and necessary condition on the weight function for the boundedness of the weighted Hardy-Littlewood average operator on Herz-type space.
出处 《数学进展》 CSCD 北大核心 2008年第5期632-636,共5页 Advances in Mathematics(China)
基金 NSFC(No.10571014) the SEDF of China(No.20040027001).
关键词 加权Hardy-Littlewood平均 MORREY-HERZ空间 HERZ空间 weighted Hardy-Littlewood average Morrey-Herz space Herz space
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参考文献12

  • 1Hardy, G., Littlewood, J. and Polya, G., Inequalities(2nd ed), London/New York: Cambridge University Press, 1952.
  • 2Anderson, K. and Muckenhoupt, B., Weighted weak type Hardy inequalities with application to Hilbert transforms and maximal functions, Studia. Math., 1982, 72: 9-26.
  • 3Levinson, N., Generalizations of an inequality of Hardy, Duke Math. J., 1964, 31: 389-394.
  • 4Martin-reyes, F. and Ortega, P., On weighted weak type inequalities for modified Hardy operators, Proc. Amer. Math. Soc., 1998, 126: 1739-1746.
  • 5Moricz, E., The harmonic Cesaro and Copson operators on the spaces, Lp, 1 ≤ p ≤ ∞, H^1 and BMO, Acta Sci. Math.(Szeged), 1999, 65: 293-310.
  • 6Muckenhoupt, B., Hardy's inequality with weights, Studia Math., 1972, 44: 31-38.
  • 7Rim, K. and Lee, J., Estimates of weighted Hardy-Littlewood averages on the p-adic vector space, J. Math. Anal. Appl., 2006, 324: 1470-1477.
  • 8Carton-Lebrun, C. and Fosset, M., Moyennes et quotients de Taylor dans BMO, Bull. Soc. Roy. Sci. Liege, 1984, 53: 85-87.
  • 9Xiao J., L^p and BMO bounds of weighted Hardy-Littlewood averages, J. Math. Anal. Appl., 2001, 262: 660-666.
  • 10Liu Z. and Fu Z., Weighted Hardy-Littlewood averages on Herz spaces, Acta Math. Sinica(Chinese Set.), 2006, 49:1085-10

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