Semigroups of Composition Operators and Integral Operators in BMOA-Type Spaces

The aim of this article is to study semigroups composition operators on the BMOA-type spaces $BMOA_p$, and their "little oh" analogues $VMOA_p$. $BMOA_p$ were introduced by R. Zhao as part large family F(p,q,s) spaces, are M\"{o}bius invariant subspaces Dirichlet $D^p_{p-1}$. We maximal subspace strong continuity, providing a sufficient condition infinitesimal generator ${\phi}$, under which $[{\phi}_t,BMOA_p]=VMOA_p$, related necessary in case where Denjoy - Wolff point semigroup $\mathbb{D}$. Further, we characterize those semigroups, for $[{\phi}_t, BMOA_p]=VMOA_p$, terms resolvent operator $T_t$. In addition provide connection between continuity Volterra-type $T_g$. symbols g $T_g$ acting from $BMOA$ $BMOA_1$ bounded or compact, thus extending result $p=1$. also prove that $1<p<2$ compactness equivalent weak compactness.