论文标题
在度量空间上限制Muckenhoupt和反向Hölder类的条件
Limiting conditions of Muckenhoupt and reverse Hölder classes on metric measure spaces
论文作者
论文摘要
自然最大和最小功能与对数的$ a_ \ infty $上的对数点数下通勤。我们使用此观察结果来表征空间$ a_1 $和$ rh_ \ infty $在公制度量空间上具有加倍措施。由于Muckenhoupt $ a_p $和反向Hölder类的限制案例，它们的行为非常对称。在一般度量测量空间上，为了通过$ a_p $和反向Hölder描述，需要一个额外的几何假设。最后，我们将表征应用于$ A_1 $和$ RH_ \ infty $的几种已知属性的简单证明，包括精致的Jones分解定理。此外，我们还显示了自然最大功能的界限。
The natural maximal and minimal functions commute pointwise with the logarithm on $A_\infty$. We use this observation to characterize the spaces $A_1$ and $RH_\infty$ on metric measure spaces with a doubling measure. As the limiting cases of Muckenhoupt $A_p$ and reverse Hölder classes, respectively, their behavior is remarkably symmetric. On general metric measure spaces, an additional geometric assumption is needed in order to pass between $A_p$ and reverse Hölder descriptions. Finally, we apply the characterization to give simple proofs of several known properties of $A_1$ and $RH_\infty$, including a refined Jones factorization theorem. In addition, we show a boundedness result for the natural maximal function.
