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My research interests lie in the interactions between operator algebras and harmonic analysis, and their connections to geometric group theory and non-commutative geometry. For more information, please see my personal homepage.
Gonzalez-Perez, A., Parcet, J. and Xia, R. (2024) Noncommutative Cotlar identities for groups acting on tree-like structures. arXiv, (doi: 10.48550/arXiv.2209.05298)
Xia, R. (2024) Geometric Interpolations for Fourier Multipliers on Groups. In: APDEGS 2021, Ghent, Belgium, 1-7 Jan 2021, pp. 395-404. ISBN 9783031570049 (doi: 10.1007/978-3-031-57005-6_41)
Xia, R. (2023) Geometric interpretations for Fourier multipliers on groups acting on trees. Science China Mathematics, 53(12), 1837. (doi: 10.1360/SSM-2023-0105)
Wu, L., Xia, R. and Zhou, D. (2023) Asymmetric Burkholder inequalities in noncommutative symmetric spaces. arXiv, (doi: 10.48550/arXiv.2201.05474)
Junge, M., Mei, T., Parcet, J. and Xia, R. (2021) Algebraic Calderón-Zygmund theory. Advances in Mathematics, 376, 107443. (doi: 10.1016/j.aim.2020.107443)
Xia, R. and Xiong, X. (2019) Mapping properties of operator-valued pseudo-differential operators. Journal of Functional Analysis, 277(9), pp. 2918-2980. (doi: 10.1016/j.jfa.2019.06.015)
Xia, R. and Xiong, X. (2019) Operator-valued local Hardy spaces. Journal of Operator Theory, 82(2), pp. 383-443.
Xia, R. and Xiong, X. (2018) Operator-valued Triebel–Lizorkin spaces. Integral Equations and Operator Theory, 90, 65. (doi: 10.1007/s00020-018-2491-1)
Xia, R. , Xiong, X. and Xu, Q. (2016) Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori. Advances in Mathematics, 291, pp. 183-227. (doi: 10.1016/j.aim.2015.12.023)
Gonzalez-Perez, A., Parcet, J. and Xia, R. (2024) Noncommutative Cotlar identities for groups acting on tree-like structures. arXiv, (doi: 10.48550/arXiv.2209.05298)
Xia, R. (2023) Geometric interpretations for Fourier multipliers on groups acting on trees. Science China Mathematics, 53(12), 1837. (doi: 10.1360/SSM-2023-0105)
Wu, L., Xia, R. and Zhou, D. (2023) Asymmetric Burkholder inequalities in noncommutative symmetric spaces. arXiv, (doi: 10.48550/arXiv.2201.05474)
Junge, M., Mei, T., Parcet, J. and Xia, R. (2021) Algebraic Calderón-Zygmund theory. Advances in Mathematics, 376, 107443. (doi: 10.1016/j.aim.2020.107443)
Xia, R. and Xiong, X. (2019) Mapping properties of operator-valued pseudo-differential operators. Journal of Functional Analysis, 277(9), pp. 2918-2980. (doi: 10.1016/j.jfa.2019.06.015)
Xia, R. and Xiong, X. (2019) Operator-valued local Hardy spaces. Journal of Operator Theory, 82(2), pp. 383-443.
Xia, R. and Xiong, X. (2018) Operator-valued Triebel–Lizorkin spaces. Integral Equations and Operator Theory, 90, 65. (doi: 10.1007/s00020-018-2491-1)
Xia, R. , Xiong, X. and Xu, Q. (2016) Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori. Advances in Mathematics, 291, pp. 183-227. (doi: 10.1016/j.aim.2015.12.023)
Xia, R. (2024) Geometric Interpolations for Fourier Multipliers on Groups. In: APDEGS 2021, Ghent, Belgium, 1-7 Jan 2021, pp. 395-404. ISBN 9783031570049 (doi: 10.1007/978-3-031-57005-6_41)
https://orcid.org/0000-0002-0516-3701