关于某种极大算子加权不等式的注记

A Note On Weighted Inequalities for a Certain Maximal Function

设，这里ｓｕｐ取所有的区间［ａ，ｂ］满足０≤ａ≤ｙ≤ｂ／φ（ｂ－ａ），φ，ｇ为某种满足给定性质的函数，我们刻划了Ｍｆ（ｙ）为弱型（Ｐ，Ｐ）的特征，同时也给出了Ｍｆ（ｙ）为强型（Ｐ，Ｐ）的一个充分条件，本文推广了文［１］和文［３］的结论，同时上述算子包含了文［２］中的某种算子。

We give a characterization for the pairs of weights (w,v) for which the maximal operator Mf (y)=sup(1/, where the supremum is taken over all intervais [a,b], such that 0≤a≤y ≤b/φ (b-a) is of weak type (P, P) with weights [w, v ),here φ,g are some given functions. In addition , a sufficient condition for strong (P, P ) is obtaLned. Our theorems contain result of paper [1] and some results of papers [2] and [3].