The Qp Carleson measure problem

Let μ be a nonnegative Borel measure on the open unit disk D⊂C. This note shows how to decide that the Möbius invariant space Qp, covering BMOA and B, is boundedly (resp., compactly) embedded in the quadratic tent-type space . Interestingly, the embedding result can be used to determine the boundedness (resp., compactness) of the Volterra-type and multiplication operators on Qp.