论文标题
Volterra型操作员将加权的Dirichlet空间映射到$ h^\ infty $
Volterra-type operators mapping weighted Dirichlet space into $H^\infty$
论文作者
论文摘要
The problem of describing the analytic functions $g$ on the unit disc such that the integral operator $T_g(f)(z)=\int_0^zf(ζ)g'(ζ)\,dζ$ is bounded (or compact) from a Banach space (or complete metric space) $X$ of analytic functions to the Hardy space $H^\infty$ is a tough problem and remains unsettled in many cases.对于具有非负MACLAURIN系数的分析功能$ G $，我们将$ t_g $从加权的dirichlet space $ d^p_Ω$作用的限制性和紧凑性，由上层加倍$ω$引起，以$ h^\ infty $。我们还表征了$ω$的整洁条件，即$ t_g：d^p_Ω\ to h^\ infty $的上升倍（或紧凑）仅当$ g $是恒定的。
The problem of describing the analytic functions $g$ on the unit disc such that the integral operator $T_g(f)(z)=\int_0^zf(ζ)g'(ζ)\,dζ$ is bounded (or compact) from a Banach space (or complete metric space) $X$ of analytic functions to the Hardy space $H^\infty$ is a tough problem and remains unsettled in many cases. For analytic functions $g$ with non-negative Maclaurin coefficients, we describe the boundedness and compactness of $T_g$ acting from a weighted Dirichlet space $D^p_ω$, induced by an upper doubling weight $ω$, to $H^\infty$. We also characterize, in terms of neat conditions on $ω$, the upper doubling weights for which $T_g: D^p_ω\to H^\infty$ is bounded (or compact) only if $g$ is constant.
