Abstract
In this paper, we completely characterize the compactness of the Volterra type integration operators \(J_b\) acting from weighted Bergman spaces \(A^p_{\alpha }\) to Hardy spaces \(H^q\) for all \(0<p,q<\infty \). Furthermore, we give some estimates for the essential norms of \(J_b:A^p_{\alpha }\rightarrow H^q\) in the case \(0<p\le q<\infty \). We finally describe the membership in the Schatten(-Herz) class of the Volterra type integration operators.
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The authors would like to thank the referee for his/her helpful comments which improved the final version of presentation.
Funding
J. Pau was partially supported by the grants MTM2017-83499-P (Ministerio de Educación y Ciencia) and 2017SGR358 (Generalitat de Catalunya). M. Wang was partially supported by NSFC (No.11771340) of China.
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Chen, J., Pau, J. & Wang, M. Essential Norms and Schatten(-Herz) Classes of Integration Operators from Bergman Spaces to Hardy Spaces. Results Math 76, 88 (2021). https://doi.org/10.1007/s00025-021-01403-8
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DOI: https://doi.org/10.1007/s00025-021-01403-8