Abstract
We investigate the boundedness and compactness of the following generalization of the Libera operator where and z 0 belongs to the closure of the unit disk 𝔻. Among other results, it is shown that if p≥1,α≥−1/p and z 0∈∂ 𝔻, the operator is bounded on the mixed norm space if and only if 1/p+(α+1)/q<1. The compactness of the operator is also investigated. We introduce two Libera-type transforms on the unit ball B⊂ℂ n . For one of these operators we give some sufficient conditions to be compact on the mixed norm space on the unit ball, and for the other we show that the operator is bounded on the weighted Bergman space on the unit ball.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
