论文标题
衍生物 - 希尔伯特操作员，作用于Dirichlet空间
A Derivative-Hilbert operator Acting on Dirichlet spaces
论文作者
论文摘要
令$μ$为间隔$ [0,1）$的积极borel量度。 hankel矩阵$ \ MATHCAL {h}_μ=（μ_{n，k}）_ {n，k \ geq 0} $带有条目$μ_{n，k} =μ__{n+k} $运算符AS $ \ Mathcal {DH}_μ（f）（z）= \ sum_ {n = 0}^\ infty \ left（\ sum_ {k = 0}^\inftyμ__{ $ f（z）= \ sum_ {n = 0}^{\ infty} a_nz^n $是$ \ mathbb {d} $中的一个分析函数。在本文中，我们表征了$ [0，1）$的那些积极的borel措施，其中$ \ nathcal {dh}_μ$从dirichlet spaces $ \ mathcal {d}_α（0 <α\ leq2）$ to $ \ mathcal to $ \ mathcal {D} d}_β（2}_β（2 <4）。
Let $μ$ be a positive Borel measure on the interval $[0,1)$. The Hankel matrix $\mathcal{H}_μ=(μ_{n,k})_{n,k\geq 0}$ with entries $μ_{n,k}=μ_{n+k}$, where $μ_{n}=\int_{[0,1)}t^ndμ(t)$, induces formally the operator as $$\mathcal{DH}_μ(f)(z)=\sum_{n=0}^\infty\left(\sum_{k=0}^\infty μ_{n,k}a_k\right)(n+1)z^n , z\in \mathbb{D},$$ where $f(z)=\sum_{n=0}^{\infty}a_nz^n$ is an analytic function in $\mathbb{D}$. In this paper, we characterize those positive Borel measures on $[0, 1)$ for which $\mathcal{DH}_μ$ is bounded (resp. compact) from Dirichlet spaces $\mathcal{D}_α( 0<α\leq2 )$ into $\mathcal{D}_β( 2\leqβ<4 )$.
