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Hadamard products in weighted Bergman spaces
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-02-01 , DOI: 10.1016/j.jmaa.2020.124617
Boban Karapetrović , Javad Mashreghi

Abstract Using the fractional derivatives D t of Hardy-Littlewood and auxiliary functions ξ γ , r and η γ , r , we study the growth of the Hadamard product f ⁎ g in the weighted Bergman space A γ q ( D ) . We precisely evaluate the growth of dilations of D α + β ( f ⁎ g ⁎ ξ γ , r ) , whenever D α f ∈ A γ p ( D ) and D β g ∈ A γ q ( D ) . The main result has numerous special cases which are interesting in their own right. In particular, we show that ‖ f ⁎ g ‖ A γ q ( D ) ≤ ‖ f ⁎ η γ , 1 ‖ A γ 1 ( D ) ‖ g ‖ A γ q ( D ) .

中文翻译:

加权伯格曼空间中的哈达玛积

摘要 利用Hardy-Littlewood 的分数阶导数D t 和辅助函数ξ γ , r 和η γ , r ,我们研究了Hadamard 乘积f ⁎ g 在加权Bergman 空间A γ q ( D ) 中的增长。我们精确地评估 D α + β ( f ⁎ g ⁎ ξ γ , r ) 膨胀的增长,无论何时 D α f ∈ A γ p ( D ) 和 D β g ∈ A γ q ( D ) 。主要结果有许多特殊情况,它们本身就很有趣。特别地,我们证明 ‖ f ⁎ g ‖ A γ q ( D ) ≤ ‖ f ⁎ η γ , 1 ‖ A γ 1 ( D ) ‖ g ‖ A γ q ( D ) 。
更新日期:2021-02-01
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