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

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