论文标题
大型伯格曼空间上的广义Volterra型积分操作员
Generalized Volterra type integral operators on large Bergman spaces
论文作者
论文摘要
令$ ϕ $为打开单位磁盘$ \ mathbb {d} $和$ g $ Analytic in $ \ mathbb {d} $的分析自动图。我们表征了广义伏尔特拉类型积分运算符的界限和紧凑性$$ gi _ {（ϕ，g）} f（z）= \ int_ {0}^{z}^{z} f'（ϕ（ϕ（ξ）） f（ϕ（ξ））\，g（ξ）\，dξ，$$在大伯格曼空间之间作用$ a^p_Ω$和$ a^q_Ω$ for $ 0 <p，q \ le \ le \ infty $。为了证明我们的特征，涉及贝雷唱型积分变换，我们使用君士坦丁和贝拉兹的Littlewood-paley公式，并建立相应的嵌入定理，这也具有独立的兴趣。当$ ϕ（z）= z $时，我们对$ gv _ {（ϕ，g）} $的结果补充了pau和peláez的描述。
Let $ϕ$ be an analytic self-map of the open unit disk $\mathbb{D}$ and $g$ analytic in $\mathbb{D}$. We characterize boundedness and compactness of generalized Volterra type integral operators $$GI_{(ϕ,g)}f(z)= \int_{0}^{z}f'(ϕ(ξ))\,g(ξ)\, dξ$$ and $$GV_{ (ϕ, g)}f(z)= \int_{0}^{z} f(ϕ(ξ))\,g(ξ)\, dξ, $$ acting between large Bergman spaces $A^p_ω$ and $A^q_ω$ for $0<p,q\le \infty$. To prove our characterizations, which involve Berezin type integral transforms, we use the Littlewood-Paley formula of Constantin and Peláez and establish corresponding embedding theorems, which are also of independent interest. When $ϕ(z) = z$, our results for $GV_{(ϕ,g)}$ complement the descriptions of Pau and Peláez.
