论文标题
加权分化构成运算符的紧凑和有限的总和
Compact and order bounded sum of weighted differentiation composition operators
论文作者
论文摘要
在本文中，我们表征了从伯格曼类型的空间到分析函数加权的Banach空间的加权分化组成算子的有界，紧凑和有界的界限，其中加权分化组成算子的总和定义为$ s^{n} _ {\ vec {\ vec {u}，（f） \ displaystyle \ sum_ {j = 0}^{n} d_ {u_ {j}，τ}^{j} {j}（f），\; \; f \ in \ Mathcal {h}（\ Mathbb d）。$$这里$ \ Mathcal {h}（\ Mathbb d）$是$ \ Mathbb d $，$ \ \ \ vec {U} = \ {j} n}的所有Holomorphic函数的空间$ u_ {j} \ in \ mathcal {h}（\ mathbb {d}）$，$τ$ a holomorphic自称为$ \ mathbb d $，$ f^{（j）} $ $ j $ j $ j $ j $ t th dter of $ f $ f $ f $ f $ and the Regishiative niviation diative contrication us $ is $ d_} $ d _}美元\; f \ in \ mathcal {h}（\ mathbb d）。$
In this paper, we characterize bounded, compact and order bounded sum of weighted differentiation composition operators from Bergman type spaces to weighted Banach spaces of analytic functions, where the sum of weighted differentiation composition operators is defined as $$ S^{n}_{\vec{u},τ}(f)= \displaystyle\sum_{j=0}^{n}D_{u_{j} ,τ}^{j}(f), \; \; f \in \mathcal{H}(\mathbb D).$$ Here $\mathcal{H}(\mathbb D)$ is the space of all holomorphic functions on $\mathbb D$, $\vec{u}=\{u_{j}\}_{j=0}^{n}$, $u_{j} \in \mathcal{H}(\mathbb{D})$, $τ$ a holomorphic self-map of $\mathbb D$, $f^{(j)}$ the $j$th derivative of $f$ and weighted differentiation composition operator $D_{u_{j},τ}^{j}$ is defined as $D_{u_{j},τ}^{j}(f)=u_{j}C_τD^{j}(f)=u_{j}f^{(j)}\circτ, \; \; f \in \mathcal{H}(\mathbb D).$
