A Toeplitz-type operator on Hardy spaces in the unit ball

Journal article, 2020

We study a Toeplitz-type operator Qμ between the holomorphic Hardy spaces Hp and Hq of the unit ball. Here the generating symbol μ is assumed to be a positive Borel measure. This kind of operator is related to many classical mappings acting on Hardy spaces, such as composition operators, the Volterra-type integration operators, and Carleson embeddings. We completely characterize the boundedness and compactness of Qμ : Hp → Hq for the full range 1 < p, q < ∞; and also describe the membership in the Schatten classes of H2. In the last section of the paper, we demonstrate the usefulness of Qμ through applications.