The closure of derivative tent spaces in the logarithmic Bloch-type norm

Abstract

In this paper, the derivative tent space \(DT_p^q(\alpha)\) is introduced. Then, we study \(\mathcal{C}_{\mathcal{B}_{{\log}^\gamma}^\beta}(DT_p^q(\alpha)\cap\mathcal{B}_{{\log}^\gamma}^\beta)\), the closure of the derivative tent space \(DT_p^q(\alpha)\) in the logarithmic Bloch-type space \(\Blog\). As a byproduct, some new characterizations for \(C_\mathcal{B}(\mathcal{D}^p_{\alpha} \cap \mathcal{B})\) and \(C_{\mathcal{B}_{{\log}}}(\mathcal{D}^2_{\alpha}\cap\mathcal{B}_{{\log}})\) are obtained.