Carleson measures for the Bloch space

In this paper we study the positive Borel measures µ on the unit disc D in C for which the Bloch space B is contin-uously included in Lp(dµ), 0 < p < ∞. We call such measures p-Bloch-Carleson measures. We give two conditions on a measure µ in terms of certain logarithmic integrals one of which is a necessary condition and the other a sufficient condition for µ being a p-Bloch-Carleson measure. We also give a complete characteriza-tion of the p-Bloch-Carleson measures within certain special classes of measures. It is also shown that, for p> 1, the p-Bloch-Carleson measures are exactly those for which the Toeplitz operator Tµ, de-fined by Tµ(f)(z) =