论文标题
由重量加倍引起的伯格曼空间上的构成操作员的紧凑差异
Compact differences of composition operators on Bergman spaces induced by doubling weights
论文作者
论文摘要
来自加权伯格曼空间$ a^p_Ω$的两个作曲运算师的有界和紧凑的差异，到lebesgue space $ l^q_ν$，其中$ 0 <q <q <q <q <p <p <\ infty $ and $Ω属于类$ \ nathcal {d} $ \ nathcal {d} $ radial radial striefts flatiage flowers flate flowers flate flowers class。在证明$ a^p_Ω$的$ q $ -carleson措施的新描述中，建立了$ p> q $和$ω\ in \ mathcal {d} $，涉及涉及伪透胶盘的$ω\。这个最后提到的结果概括了经典加权伯格曼空间$ Q $ -CARLESON措施的众所周知的特征，并在倍增权重的设置中，$ -1 <α<\ infty $。还简要讨论了\ wideHat {\ mathcal {d}} $的情况$ω\ in \ wideHat {\ mathcal {d}} $，并提出了有关此情况的开放问题。
Bounded and compact differences of two composition operators acting from the weighted Bergman space $A^p_ω$ to the Lebesgue space $L^q_ν$, where $0<q<p<\infty$ and $ω$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling condition, are characterized. On the way to the proofs a new description of $q$-Carleson measures for $A^p_ω$, with $p>q$ and $ω\in\mathcal{D}$, involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of $q$-Carleson measures for the classical weighted Bergman space $A^p_α$ with $-1<α<\infty$ to the setting of doubling weights. The case $ω\in\widehat{\mathcal{D}}$ is also briefly discussed and an open problem concerning this case is posed.
