Vanishing Carleson-type measures defined with additional logarithmic terms are characterized by using functions in $BMOA$ and the Bloch space. The results are applied to Cesáro type operators on $BMOA$ and the Bloch space.
"Vanishing logarithmic Carleson measures." Illinois J. Math. 46 (2) 507 - 518, Summer 2002. https://doi.org/10.1215/ijm/1258136207