On some equivalent definitions of $\rho$- Carleson measures on the unit ball

Abstract

We give in this paper some equivalent definitions of the so called $\rho$-Carleson measures when $\rho (t)=(\log (4/t){)}^p(\log \log (e^4/t){)}^q$, $0\le p,q<\infty$. As applications, we characterize the pointwise multipliers on $LMOA({\mathbb{S}}^n)$ and from this space to $BMOA({\mathbb{S}}^n)$. Boundedness of the Cesàro type integral operators on $LMOA({\mathbb{S}}^n)$ and from $LMOA({\mathbb{S}}^n)$ to $BMOA({\mathbb{S}}^n)$ is considered as well.

arXiv comment23 pages