Research

My research concerns harmonic analysis, microlocal analysis, partial differential equations and functional analysis.

Current and former research topics:

1. Harmonic analysis and microlocal analysis
   - L^p regularity of Fourier integral operators: invariant spaces for Fourier integral operators and local smoothing.
2. Partial differential equations
   - Rough wave equations: L^p regularity of wave equations with rough coefficients.
   - Nonlinear wave equations: well-posedness for initial data outside of L²-based Sobolev spaces. 
3. Functional analysis and operator theory
   - Semigroup theory: asymptotic behavior of C₀-semigroups and functional calculus theory. 
   - Harmonic analysis in Banach spaces: operator-valued Fourier multipliers.
   - Noncommutative analysis: operator Lipschitz functions.
   - Positivity: representations of groups as lattice isomorphisms on L^p spaces.

Journal publications (preprint versions available here):

1. Local smoothing and Hardy spaces for Fourier integral operators on manifolds. J. Funct. Anal. 286 (2024), no. 2, Paper No. 110221, 72 pp. With Naijia Liu, Liang Song and Lixin Yan.
2. L^p and H^p_FIO regularity for wave equations with rough coefficients. Pure Appl. Anal. 5 (2023), no. 3, 541-599. With Andrew Hassell.
3. Rough pseudodifferential operators on Hardy spaces for Fourier integral operators. J. Anal. Math. 149 (2023), no. 1, 135-165.
4. Characterizations of the Hardy space H¹_FIO for Fourier integral operators. Studia Math. 270 (2023), no. 2, 175-207. With Zhijie Fan, Naijia Liu and Liang Song.
5. Nonlinear wave equations with slowly decaying initial data. J. Differential Equations 350 (2023), 152-188. With Robert Schippa.
6. Operator-valued (L^p,L^q) Fourier multipliers and stability theory for evolution equations. Indag. Math. 34 (2023), no. 1, 1-36.
7. Local smoothing and Hardy spaces for Fourier integral operators. J. Funct. Anal. 283 (2022), no. 12, Paper No. 109721, 22 pp.
8. Rough pseudodifferential operators on Hardy spaces for Fourier integral operators II. J. Fourier Anal. Appl. 28 (2022), no. 4, Paper No. 65, 27 pp.
9. Characterizations of Hardy spaces for Fourier integral operators. Rev. Mat. Iberoam. 37 (2021), no. 5, 1717-1745.
10. ​Off-singularity bounds and Hardy spaces for Fourier integral operators. Trans. Amer. Math. Soc. 373 (2020), no. 8, 5773-5832. With Andrew Hassell and Pierre Portal.
11. Functional calculus for C₀-groups using type and cotype. Q. J. Math. 70 (2019), no. 1, 17-47.
12. Optimal rates of decay for operator semigroups on Hilbert spaces. Adv. Math. 346 (2019), 359-388. With David Seifert and Reinhard Stahn.
13. Sharp growth rates for semigroups using resolvent bounds. J. Evol. Equ. 18 (2018), no. 4, 1721-1744. With Mark Veraar.
14. Stability theory for semigroups using (L^p,L^q) Fourier multipliers. J. Funct. Anal. 275 (2018), no. 10, 2845-2894. With Mark Veraar.
15. Fourier multiplier theorems involving type and cotype. J. Fourier Anal. Appl. 24 (2018), no. 2, 583-619. With Mark Veraar.
16. Fourier multiplier theorems on Besov spaces under type and cotype conditions. Banach J. Math. Anal. 11 (2017), no. 4, 713-743. With Mark Veraar.
17. Disintegration of positive isometric group representations on L^p-spaces. Positivity 21 (2017), no. 2, 673-710. With Marcel de Jeu.
18. Operator Lipschitz functions on Banach spaces. Studia Math. 232 (2016), no. 1, 57-92. With Fedor Sukochev and Anna Tomskova.
19. Functional calculus on real interpolation spaces for generators of C₀-groups. Math. Nachr. 289 (2016), no. 2-3, 275-289. With Markus Haase.
20. Functional calculus for semigroup generators via transference. J. Funct. Anal. 265 (2013), no. 12, 3345-3368. With Markus Haase.
21. Convergence of subdiagonal Padé approximations of C₀-semigroups. J. Evol. Equ. 13 (2013), no. 4, 875-895. With Moritz Egert.

Preprints:

1. Improved polynomial decay for unbounded semigroups. 2024, 14 pages. Available here. With Chenxi Deng and Mark Veraar.
2. Spherical maximal functions and Hardy spaces for Fourier integral operators. 2024, 32 pages. Available here. With Abhishek Ghosh, Naijia Liu and Liang Song.
3. Function spaces for decoupling. 2023, 41 pages. Available here. With Andrew Hassell, Pierre Portal and Po-Lam Yung.

Theses:

1. Harmonic analysis on Banach spaces and stability theory for evolution equations. Habilitation essay, 2021, 32 pages. Available here.
2. Functional Calculus via Transference, Double Operator Integrals and Applications. PhD thesis, 2015, ISBN 978-94-6259-800-3, vi+175 pages. Available here.
3. Decomposing positive representations in L^p-spaces for Polish transformation groups. Master thesis, 2011, 52 pages. Available here.
4. A space of spaces. Bachelor thesis, 2010, 19 pages. Available here.

Lecture notes:

1. The approximation property. 2012, 14 pages. Available here.

Typos and mistakes in published articles:

Here is a list.