Analytic Function Spaces Associated with the p-Carleson Measure for the Bloch Space

Abstract

We investigate the p-Carleson measure for the Bloch space \({\mathcal {B}}\) and introduce a holomorphic function space \( W_{\mathcal {B}}^{p,\alpha }\) associated with this measure. An integral operator which preserves the p-Carleson measure for \({\mathcal {B}}\) is established. As applications, we give a generalized Jones’ formula for \( W_{\mathcal {B}}^{p,\alpha }\) , characterize the bounded small Hankel operator \(h_{s,f}\) from \({\mathcal {B}}\) to the Bergman space \(A_\alpha ^p\) , and give an atomic decomposition of \( W_{\mathcal {B}}^{p,\alpha }\) .