Abstract
We study composition operators acting between Hardy spaces \(H^p(\Omega )\), where \(\Omega \subset \mathbb {C}^2\) is a smoothly bounded, \(\mathbb {C}\)-linearly convex domain admitting the so-called F-type at all boundary points. This F-type domains contain certain convex domains of finite type and many cases of infinite type in the sense of Range. Criteria for boundedness and compactness of such composition operators are established. Our approach is based on the Cauchy–Leray kernel.
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Acknowledgements
This article was carried out during the first-named author’s stay at Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, as a postdoc fellow under the MOE’s AcRF Tier 1 M4011724.110 (RG128/16). He thanks the institution for hospitality and support. The authors would like to thank the referees for useful remarks and comments that led to the improvement of the paper.
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Communicated by Irene Sabadini, Michael Shapiro, Daniele Struppa and Daniel Alpay.
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Funded by Vietnam National University HoChiMinh City (VNU-HCM) under Grant Number B2019-18-01.
Supported in part by MOE’s AcRF Tier 1 M4011724.110 (RG128/16).
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Ha, L.K., Khoi, L.H. Composition Operators Between Hardy Spaces on Linearly Convex Domains in \(\mathbb {C}^2\). Complex Anal. Oper. Theory 13, 2589–2603 (2019). https://doi.org/10.1007/s11785-019-00926-x
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DOI: https://doi.org/10.1007/s11785-019-00926-x
Keywords
- Hardy space
- Composition operator
- \(\mathbb {C}\)-linearly convex domain
- Infinite type
- Cauchy–Fantappiè form
- Cauchy–Leray kernel