论文标题
从谐波伯格曼 - 巴索夫空间到另一个
Positive Toeplitz Operators from a Harmonic Bergman-Besov space into Another
论文作者
论文摘要
我们在$ \ Mathbb {r}^n $的单位球上定义了正toeplitz运算符$ b^p_α$，用于全部参数$ 0 <p <\ infty $，$α\ in \ mathbb {r} $。我们将有界和紧凑的Toeplitz操作员的特征在于Carleson和消失的Carleson措施方面，将一个谐波Bergman-Besov空间带入另一个谐波。我们还为$ b^{2}_α$在平均函数方面为$ b^{2}_α$上的正面toeplitz运算符提供了特征，以$ 1 \ leq p <\ leq p <\ leq p <\ leq p <\ leq p <\ leq p <\ in \ in \ mathbb in \ mathbb {r r} $。我们的结果扩展了以谐波加权伯格曼空间而闻名的结果。
We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_α$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $α\in\mathbb{R}$. We give characterizations of bounded and compact Toeplitz operators taking one harmonic Bergman-Besov space into another in terms of Carleson and vanishing Carleson measures. We also give characterizations for a positive Toeplitz operator on $b^{2}_α$ to be a Schatten class operator $S_{p}$ in terms of averaging functions and Berezin transforms for $1\leq p<\infty$, $α\in\mathbb{R}$. Our results extend those known for harmonic weighted Bergman spaces.
