A Toeplitz type operator on Hardy spaces in the unit ball

2018/05/11 by Pau, Jordi, Perälä, Antti
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1805.04339

Abstract

We study a Toeplitz type operator Q_μ between the holomorphic Hardy spaces H^p and H^q of the unit ball. Here the generating symbol μ is assumed to 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_μ:H^p→ H^q for the full range 1

Related

• Toeplitz operators on the unit ball with locally integrable symbols
• Composition Operators on \bf H^p,q,s(B_n) of \bf ℂⁿ
• Integration operators between Hardy spaces on the unit ball of \Cn
• Toeplitz and Hankel operators between distinct Hardy spaces
• Tent Carleson measures for Hardy spaces