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

Pau, Jordi; Perälä, Antti

doi:10.1090/tran/8053

A Toeplitz-type operator on Hardy spaces in the unit ball
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by Jordi Pau and Antti Perälä PDF

Trans. Amer. Math. Soc. 373 (2020), 3031-3062 Request permission

Abstract:

We study a Toeplitz-type operator $Q_\mu$ between the holomorphic Hardy spaces $H^p$ and $H^q$ of the unit ball. Here the generating symbol $\mu$ 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 $Q_\mu :H^p\to H^q$ for the full range $1<p,q<\infty$; and also describe the membership in the Schatten classes of $H^2$. In the last section of the paper, we demonstrate the usefulness of $Q_\mu$ through applications.

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