The $\mathcal{Q}_p$ Carleson Measure Problem
Abstract
Description
Let $μ$ be a nonnegative Borel measure on the open unit disk $\mathbb{D}\subset\mathbb{C}$. This note shows how to decide that the Möbius invariant space $\mathcal{Q}_p$, covering $\mathcal{BMOA}$ and $\mathcal{B}$, is boundedly (resp., compactly) embedded in the quadratic tent-type space $T^\infty_p(μ)$. Interestingly, the embedding result can be used to determine the boundedness (resp., the compactness) of the Volterra-type and multiplication operators on $\mathcal{Q}_p$.
12 pages
12 pages