In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and ...In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.展开更多
We give a condition on the couple of weights（u,v） for Doob＇s operator to be a bounded one from martingale space Lp（u） to function space Lp（v） .Moreover,we also obtain necessary and sufficient conditions in orde...We give a condition on the couple of weights（u,v） for Doob＇s operator to be a bounded one from martingale space Lp（u） to function space Lp（v） .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp（u） to function space Lp（v） or Lp,∞（v） .展开更多
基金supported by the NSF of China and the aid financial plan for the backbone of the young teachers of university of Henan
文摘In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M0^＊, then they give sufficient conditions under which the equality M0=MM0^＊ holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W∞^＊-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.
基金Supported by the National Natural Science Foundation of China(10671147)
文摘We give a condition on the couple of weights（u,v） for Doob＇s operator to be a bounded one from martingale space Lp（u） to function space Lp（v） .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp（u） to function space Lp（v） or Lp,∞（v） .
