On an integral-type operator acting between Bloch-type spaces on the unit ball
Let \(\mathbb B\) denote the open unit ball of \(\mathbb C^n\). For a holomorphic self-map \(\varphi\) of \(\mathbb B\) and a holomorphic function \(g\) in \(\mathbb B\) with \(g(0)=0\), we define the following integral-type operator: \(I_\varphi^g f(z)=\int^1_0 \Re f(\varphi(tz))g(tz)(dt/t)\), \(z\in\mathbb B\). Here \(\Re f\) denotes the radial derivative of a holomorphic function \(f\) in \(\mathbb B\). We study the boundedness and compactness of the operator between Bloch-type spaces \({\mathcal B}\omega\) and \({\mathcal B}\mu\), where \(\omega\) is a normal weight function and \(\mu\) is a weight function. Also, we consider the operator between the little Bloch-type spaces \({\mathcal B}_{\omega,0}\) and \({\mathcal B}_{\mu,0}\).
scientific article; zbMATH DE number 5791606
scientific article