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.