论文标题
通过加倍的伯格曼空间上的广义加权构图操作员
Generalized weighted composition operators on Bergman spaces induced by doubling weights
论文作者
论文摘要
从加权Bergman空间$ a^p_Ω$行动的有界和紧凑的广义加权构图运算符，其中$ 0 <p <\ infty $和$ω$属于radial radial重量的类$ \ Mathcal {D} $ class $ l^q_ u^q_ us l^q_ c_的radial flowers class $ \ mathcal {d} $。在通往证据的途中，建立了加权伯格曼空间上的新定理$ a^p_Ω$。这种最后提及的结果概括了分化操作员的界限$ d^n（f）= f^{（n）} $从经典加权的伯格曼空间$ a^p_α$ to lebesgue space $ l^q_μ$引起的，该$ l^q_μ$，由积极的borel borel Matues $μ$μ$μ$μ$，到设置调高量的重量。
Bounded and compact generalized weighted composition operators acting from the weighted Bergman space $A^p_ω$, where $0<p<\infty$ and $ω$ belongs to the class $\mathcal{D}$ of radial weights satisfying a two-sided doubling condition, to a Lebesgue space $L^q_ν$ are characterized. On the way to the proofs a new embedding theorem on weighted Bergman spaces $A^p_ω$ is established. This last-mentioned result generalizes the well-known characterization of the boundedness of the differentiation operator $D^n(f)=f^{(n)}$ from the classical weighted Bergman space $A^p_α$ to the Lebesgue space $L^q_μ$, induced by a positive Borel measure $μ$, to the setting of doubling weights.
