论文标题
几何最大运算符和产品基础上的BMO
Geometric maximal operators and BMO on product bases
论文作者
论文摘要
我们考虑了$ \ mathbb {r}^n $上最大运算符在BMO上的最大运算符有限性的问题。我们证明，对于具有吞噬特性的形状碱基，相应的最大函数从BMO到BLO界定，从而概括了Bennett的已知结果以基于立方体的基础。当形状的基础不具有吞噬特性，而是表现出相对于具有吞噬特性的碱基的较低尺寸形状的产物结构时，我们表明，相应的最大函数从BMO到我们定义和调用矩形矩形blo的空间界定。
We consider the problem of the boundedness of maximal operators on BMO on shapes in $\mathbb{R}^n$. We prove that for bases of shapes with an engulfing property, the corresponding maximal function is bounded from BMO to BLO, generalising a known result of Bennett for the basis of cubes. When the basis of shapes does not possess an engulfing property but exhibits a product structure with respect to lower-dimensional shapes coming from bases that do possess an engulfing property, we show that the corresponding maximal function is bounded from BMO to a space we define and call rectangular BLO.
