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Carleson measures for the Dirichlet–Orlicz space

Volume 240 / 2018

Maria Rosaria Tupputi 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 $(\mathbb D, \mu )$.

Authors

  • Maria Rosaria TupputiDipartimento di Statistica e Metodi Quantitativi (DiSMeQ)
    Università di Milano-Bicocca
    Bicocca degli Arcimboldi 8
    Milano, Italy
    e-mail

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