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 N. Liu, L. Song and L. 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 A. 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 Z. Fan, N. Liu and L. Song.
5. Nonlinear wave equations with slowly decaying initial data. J. Differential Equations 350 (2023), 152-188. With R. 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 A. Hassell and P. 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 D. Seifert and R. Stahn.
13. Sharp growth rates for semigroups using resolvent bounds. J. Evol. Equ. 18 (2018), no. 4, 1721-1744. With M. Veraar.
14. Stability theory for semigroups using (L^p,L^q) Fourier multipliers. J. Funct. Anal. 275 (2018), no. 10, 2845-2894. With M. Veraar.
15. Fourier multiplier theorems involving type and cotype. J. Fourier Anal. Appl. 24 (2018), no. 2, 583-619. With M. Veraar.
16. Fourier multiplier theorems on Besov spaces under type and cotype conditions. Banach J. Math. Anal. 11 (2017), no. 4, 713-743. With M. Veraar.
17. Disintegration of positive isometric group representations on L^p-spaces. Positivity 21 (2017), no. 2, 673-710. With M. de Jeu.
18. Operator Lipschitz functions on Banach spaces. Studia Math. 232 (2016), no. 1, 57-92. With F. Sukochev and A. Tomskova.
19. Functional calculus on real interpolation spaces for generators of C₀-groups. Math. Nachr. 289 (2016), no. 2-3, 275-289. With M. Haase.
20. Functional calculus for semigroup generators via transference. J. Funct. Anal. 265 (2013), no. 12, 3345-3368. With M. Haase.
21. Convergence of subdiagonal Padé approximations of C₀-semigroups. J. Evol. Equ. 13 (2013), no. 4, 875-895. With M. Egert.

Preprints:

1. Spherical maximal functions and Hardy spaces for Fourier integral operators. 2024, 32 pages. Available here. With A. Ghosh, N. Liu and L. Song.
2. Function spaces for decoupling. 2023, 41 pages. Available here. With A. Hassell, P. Portal and P.-L. 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.