Abstract
In this paper, we introduce an algebra of singular integral operators containing Bessel potentials of positive order, and show that the corresponding unital Banach algebra is an inverse-closed Banach subalgebra of \({\mathcal {B}} (L^q_w)\), the Banach algebra of all bounded operators on the weighted space \(L_w^q\), for all \(1\le q<\infty \) and Muckenhoupt \(A_q\)-weights \(w\).
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Acknowledgments
The authors would like to thank anonymous reviewers for their comments and suggestions. The authors are partially supported by the Scientific Project of Zhejiang Provincial Science Technology Department fundeded by NSF of China (#2011C33012, Project 11071065), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0027339), and National Science Foundation (DMS-1109063).
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Communicated by K. Gröchenig.
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Fang, Q., Shin, C.E. & Sun, Q. Wiener’s lemma for singular integral operators of Bessel potential type. Monatsh Math 173, 35–54 (2014). https://doi.org/10.1007/s00605-013-0575-1
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DOI: https://doi.org/10.1007/s00605-013-0575-1