关于广义g-函数的BMO有界性

Boundedness of the Generalized g-Function on BMO(R^n)

本文的主要结果如下：设g_r（f）为一广义g-函数，2≤r＜∞，f∈BMO（Rn），若gr（f）在某一正测度集上有限，则gr（f）几乎处处有限，且存在与f无关的常数C使得｜｜gr(f)｜｜．≤C｜｜f｜｜．．

In this paper, we proved the following result: Let gr (f) be a generalized g-function (2≤r＜∞ ),and f∈ BMO (Rn). If gr (f) (x) ＜∞ for all x∈E, which is a set with positive measure,then gr(f) (x) is finite almost everywhere in Rn,and there is a constant C such that: ｜｜ gr(f) ｜｜*≤C｜｜f||*.