Generalized hilbert operator on bergman spaces
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초록
We consider the generalized Hilbert operator $\mathcal{H_\beta}$ for $\beta\geq 0$ and find the condition on the parameter $\beta$ for which the operator $\mathcal{H_\beta}$ is bounded on the Bergman space $ A^p$ for $2<p<\infty$. Also, we estimates the upper bound of the norm on $A^p$. Further shows that $\mathcal{H_\beta}$ is not bounded on $ A^2$ for $0\leq\beta<1.$
Abstract
We consider the generalized Hilbert operator $\mathcal{H_\beta}$ for $\beta\geq 0$ and find the condition on the parameter $\beta$ for which the operator $\mathcal{H_\beta}$ is bounded on the Bergman space $ A^p$ for $2<p<\infty$. Also, we estimates the upper bound of the norm on $A^p$. Further shows that $\mathcal{H_\beta}$ is not bounded on $ A^2$ for $0\leq\beta<1.$