Let $0 \lt p,s \lt \infty $, $n$ be a nonnegative integer and $\mu $ be a positive Borel measure on $\mathbb {D}$. Let $\mathcal {T}_{s}^{p,n}{(\mu )}$ be the space of all analytic functions $f $ such that $$\sup _{I\subseteq \partial \mathbb D}\frac {1}{

Let mu be a nonnegative Borel measure on the unit disk D. In this paper, we investigate measures mu such that the weighted BMOA spaces are embedded boundedly or compactly into tent-type spaces T-phi(infinity)(mu). As an application, we characterize the boundedness and compactness of Volterra integral operators on the weighted BMOA space.

Suppose $$(C_t)_{t\geqslant 0}$$ ( C t ) t ⩾ 0 is the composition semigroup induced by a one-parameter semigroup $$(\varphi _t)_{t\geqslant 0}$$ ( φ t ) t ⩾ 0 of analytic self-maps of the unit disk. The main purpose of the paper is to investigate the spectrum of the infinitesimal generator of $$(C_t)_{t\geqslant 0}$$ ( C t ) t ⩾ 0 acting on the weighted Bergman space induced by doubling weights, provided $$(\varphi _t)_{t\geqslant 0}$$ ( φ t ) t ⩾ 0 is elliptic. The method applied is a certain spectral mapping theorem and a characterization of the spectra of certain composition operators. Eventual norm-continuity of $$(C_t)_{t\geqslant 0}$$ ( C t ) t ⩾ 0 also plays an important role, which can be depicted in terms of studying the difference of two distinct composition operators. As a byproduct, we also characterize a certain compact integral operator that is closely related to the resolvent of the infinitesimal generator of $$(C_t)_{t\geqslant 0}$$ ( C t ) t ⩾ 0 .