论文标题
经典分析功能空间上广义希尔伯特矩阵运算符的确切基本规范
Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces
论文作者
论文摘要
我们计算了作用于加权伯格曼空间$ a^p_v $和加权的Banach空间$ h^\ infty_v $的总体上的普遍性矩阵运算符的基本规范的确切价值，其中$ v $是一般径向的重量。特别是，我们获得了标准加权的伯格曼（Bergman）空间$ a^p_α$ for $ p> 2+α，\，\，α\ ge 0，$和korenblum spaces $ h^\infty_α$ for $ 0 <α<1 <1 <1 <1 <1 <1 p> p p> p p，在加权的伯格曼空间案例中，希尔伯特矩阵的基本规范等于其运算符规范的猜想值，并且在强壮的空间案例中类似，基本规范和操作员的范围重合。我们还计算了$ h^\ infty_ {w_α} $的Hilbert Matrix的确切值，而权重$W_α（Z）=（1- | Z |）^α$，用于所有$ 0 <α<1 $。同样在这种情况下，规范和基本规范的值一致。
We compute the exact value of the essential norm of a generalized Hilbert matrix operator acting on weighted Bergman spaces $A^p_v$ and weighted Banach spaces $H^\infty_v$ of analytic functions, where $v$ is a general radial weight. In particular, we obtain the exact value of the essential norm of the classical Hilbert matrix operator on standard weighted Bergman spaces $A^p_α$ for $p>2+α, \, α\ge 0,$ and on Korenblum spaces $H^\infty_α$ for $0 < α< 1.$ We also cover the Hardy space $H^p, \, 1 < p < \infty,$ case. In the weighted Bergman space case, the essential norm of the Hilbert matrix is equal to the conjectured value of its operator norm and similarly in the Hardy space case the essential norm and the operator norm coincide. We also compute the exact value of the norm of the Hilbert matrix on $H^\infty_{w_α}$ with weights $w_α(z)=(1-|z|)^α$ for all $0 < α< 1$. Also in this case, the values of the norm and essential norm coincide.
