论文标题
谐波伯格曼投影仪上的均匀树木
Harmonic Bergman projectors on homogeneous trees
论文作者
论文摘要
在本文中，我们研究了$ q $ - 均匀树上的谐波伯格曼空间$ \ mathcal a^p（σ）$的某些属性，其中$ q \ geq 2 $，$ 1 \ leq p <\ iffty $，$σ$是辐射降低密度的降低密度，nondembount，nondemplous的有限量。这些空间由J.〜Cohen，F .〜Colonna，M。〜Picardello和D.〜Singman引入。当$ p = 2 $时，他们正在繁殖内核希尔伯特空间，我们明确计算其繁殖核。然后，我们研究伯格曼投影仪在$ l^p（σ）$上的有界性能，价格为$ 1 <p <\ infty $及其弱类型（1,1）的界限，以呈径向指数降低树上的措施。弱类型（1,1）的界限是伯格曼内核满足适当整体Hörmander状况的结果。
In this paper we investigate some properties of the harmonic Bergman spaces $\mathcal A^p(σ)$ on a $q$-homogeneous tree, where $q\geq 2$, $1\leq p<\infty$, and $σ$ is a finite measure on the tree with radial decreasing density, hence nondoubling. These spaces were introduced by J.~Cohen, F.~Colonna, M.~Picardello and D.~Singman. When $p=2$ they are reproducing kernel Hilbert spaces and we compute explicitely their reproducing kernel. We then study the boundedness properties of the Bergman projector on $L^p(σ)$ for $1<p<\infty$ and their weak type (1,1) boundedness for radially exponentially decreasing measures on the tree. The weak type (1,1) boundedness is a consequence of the fact that the Bergman kernel satisfies an appropriate integral Hörmander's condition.
