Abstract. Carleson type measures with additional logarithmic terms are characterized by using functions in $BMOA$ and the Bloch space. The results are applied to a kind of integral operators and pointwise multipliers on $BMOA$ and the Bloch space, as well as Toeplitz operators on the weighted Bergman $1$-space.

AMS Subject Classification (1991): 30D50; 30D45, 47B35

Keyword(s): logarithmic Carleson measure, BMOA, pointwise multipliers, Bloch space

Received February 20, 2002, and in revised form July 19, 2002. (Registered under 2919/2009.)