Abstract
We consider the dual Toeplitz operators acting on the orthogonal complements of Hardy–Sobolev spaces of the unit ball. We first characterize the compactness of finite sums of dual Toeplitz products. Using this result, we next study the problem of when finite sums of products of two dual Toeplitz operators is another dual Toeplitz operator. Our results extend several known results on the Dirichlet spaces to the Hardy–Sobolev spaces.
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Communicated by Tao Qian.
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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.
L. He and P. Y. Huang were supported by National Natural Science Foundation of China (No. 11871170), the open project of Key Laboratory, school of Mathematical Sciences, Chongqing Normal University (No. CSSXKFKTM202002) and the Innovation Research for the Postgraduates of Guangzhou University (No. 2020GDJC-M29). Also, Y. J. Lee was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1I1A3A01041943). We are co-first authors.
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He, L., Huang, P. & Lee, Y.J. Sums of Dual Toeplitz Products on the Orthogonal Complements of the Hardy–Sobolev Spaces. Complex Anal. Oper. Theory 15, 119 (2021). https://doi.org/10.1007/s11785-021-01170-y
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DOI: https://doi.org/10.1007/s11785-021-01170-y