Integral operators and Carleson measures for Möbius invariant Besov spaces

Abstract

We investigate an integral operator \(T_{t,\lambda}\) which preserves the Carleson measure for the Möbius invariant Besov space \(B_p\) on the unit ball of \(\mathbb{C}^{n}\). A holomorphic function space \(W_\beta^p\), associated with the Carleson measure for \(B_p\), is introduced. As applications for the operator \(T_{t,\lambda}\), we estimate the distance from Bloch-type functions to the space \(W_\beta^p\), which extends Jones' formula. Moreover, the bounded small Hankel operators on \(B_p\) and the atomic decomposition of \(W_\beta^p\) are characterized.