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.

Hardy spaces

Schatten classes

Tent spaces

Toeplitz operators

Author

Jordi Pau

University of Barcelona

Antti Perälä

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Transactions of the American Mathematical Society

0002-9947 (ISSN) 1088-6850 (eISSN)

Vol. 373 5 3031-3062

Subject Categories

Mathematics

DOI

10.1090/tran/8053

More information

Latest update

4/28/2020