Carleson measures for the Dirichlet–Orlicz space
Volume 240 / 2018
Studia Mathematica 240 (2018), 1-20
MSC: Primary 46E35; Secondary 46E30, 31C25.
DOI: 10.4064/sm8274-3-2017
Published online: 31 August 2017
Abstract
We introduce the Dirichlet–Orlicz space as the space of holomorphic functions on the open complex unit disk $\mathbb D$ having the Orlicz norm of their first derivative finite. Then we characterize by means of Carleson type boxes the positive $\sigma $-finite measures $\mu $ which realize the embeddings of the Dirichlet–Orlicz space into classical Orlicz spaces defined on the measure space $(\mathbb D, \mu )$.
