论文标题
加权均匀树上的BMO空间
BMO spaces on weighted homogeneous trees
论文作者
论文摘要
我们认为一棵无限的同质树$ \ Mathcal V $赋予了图表上定义的通常的度量$ d $和加权度量$μ$。度量测量空间$（\ Mathcal V，d，μ）$是非倍的，并且指数增长，因此在这种情况下不适用Hardy和$ bmo $ spaces的经典理论。我们在$（\ Mathcal V，d，μ）上引入了Space $ bmo（μ）$，并调查了其一些属性。我们特别证明，可以用$ bmo（μ）$识别出在先前工作中引入的hardy space $ h^1（μ）$的双重识别，我们研究了与$ bmo（μ）$相关的尖锐最大功能。
We consider an infinite homogeneous tree $\mathcal V$ endowed with the usual metric $d$ defined on graphs and a weighted measure $μ$. The metric measure space $(\mathcal V,d,μ)$ is nondoubling and of exponential growth, hence the classical theory of Hardy and $BMO$ spaces does not apply in this setting. We introduce a space $BMO(μ)$ on $(\mathcal V,d,μ)$ and investigate some of its properties. We prove in particular that $BMO(μ)$ can be identified with the dual of a Hardy space $H^1(μ)$ introduced in a previous work and we investigate the sharp maximal function related with $BMO(μ)$.
