A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES
A NOTE ON WEIGHTED NORM INEQUALITIES FOR FRACTIONAL MAXIMAL OPERATORS WITH NON-DOUBLING MEASURES
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DOI：
10.11650/twjm/1500406741
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发表时间：
2012-01
影响因子：
0.4
通讯作者：
Weihong Wang;Chaoqiang Tan;Zengjian Lou
中科院分区：
文献类型：
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作者：
Weihong Wang;Chaoqiang Tan;Zengjian Lou
设$\mu$是$\mathbb{R}^d$上的非负Borel测度，且仅满足一定的增长条件，研究了与$\mu$相关的分数阶极大函数的双权范数不等式.给出了极大算子从$L^p（v）$到弱$L^{q}（u）$（1\leqp\leqq <\infty）$有界的一个充要条件.进一步利用Orlicz范数，得到了一个强型不等式.
Let $\mu$ be a non-negative Borel measure on $\mathbb{R}^d$ which only satisfies some growth condition, we study two-weight norm inequalities for fractional maximal functions associated to such $\mu$. A necessary and sufficient condition for the maximal operator to be bounded from $L^p(v)$ into weak $L^{q}(u)$ $(1\leq p\leq q<\infty)$ is given. Furthermore, by using certain Orlicz norm, a strong type inequality is obtained.