Abstract. We give here 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 $LMOA({\msbm S}^n)$ and from this space to $BMOA({\msbm S}^n)$. Boundedness of the Cesàro type integral operators on $LMOA({\msbm S}^n)$ and from $LMOA({\msbm S}^n)$ to $BMOA({\msbm S}^n)$ is considered as well.
AMS Subject Classification
(1991): 28A25; 30D45; 30D50; 47B38
Keyword(s):
Carleson measures,
Hardy spaces,
Bergman spaces,
Bloch spaces,
BMOA,
LMOA
Received September 26, 2008, and in final form January 28, 2009. (Registered under 6426/2009.)
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