Essential norm of generalized Hilbert matrix from Bloch type spaces to BMOA and Bloch space

Abstract

Let $ \mu $ be a positive Borel measure on the interval $ [0, 1) $. The Hankel matrix $ {\mathcal H}_\mu = (\mu_{n+k})_{n, k\geq 0} $ with entries $ \mu_{n, k} = \mu_{n+k} $ induces the operator $ {\mathcal H}_\mu(f)(z) = \sum\limits_{n = 0}^\infty\left(\sum\limits_{k = 0}^\infty\mu_{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}_\mu $ from Bloch type spaces to the BMOA and the Bloch space. Moreover we obtain the essential norm of $ {\mathcal H}_\mu $ from $ {\mathcal{B}}^\alpha $ to $ {\mathcal{B}} $ and BMOA.