Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space
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 $μ_{n,k}=μ_{n+k}$ induces the operator $$ \mathcal{H}_μ(f)(z)=\sum^\infty_{n=0}\left(\sum^\infty_{k=0}μ_{n,k}a_k\right)z^n $$ on the space of all analytic functions $f(z)=\sum^\infty_{n=0}a_nz^n$ in the unit disk $\mathbb{D}$. In this paper, we characterize the boundedness and compactness of $\mathcal{H}_μ$ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $\mathcal{H}_μ$ from $α$ Bloch type spaces to Bloch space and BMOA.
math.CV↗