左红亮; 刘培德
Zuo Hongliang; Liu Peide
摘要:
In this article, the authors introduce two operators---geometrical maximal operator M0 and the closely related limiting operator M*0, then they give sufficient conditions under which the equality M0=M*0 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.
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