Function spaces for local smoothing

Project data:

Sonata 17 grant 2021/43/D/ST1/00667.
Financed by the National Science Centre, Poland.
03-10-2022 to 02-10-2025.
970,740 PLN.
 

Project goal:

The project concerns the construction and use of new function spaces to study local smoothing for wave equations. This builds upon work which connects local smoothing estimates for the Euclidean wave equation, as well as the l^p decoupling inequality for the light cone, to the Hardy spaces for Fourier integral operators.
For a more accessible (albeit imprecise) description, see here (i po polsku).
 

Project team:

1. Jan Rozendaal. Principal Investigator.
2. Abhishek Ghosh. Postdoctoral Fellow.

Research output:

1. Spherical maximal functions and Hardy spaces for Fourier integral operators. 2024, 32 pages. Available here. By A. Ghosh, N. Liu, J. Rozendaal and L. Song.
2. Decay at infinity for solutions to some fractional parabolic equations. Proc. Roy. Soc. Edinburgh Sect. A (2024), 1-37. Published online. By A. Ghosh and A. Banerjee. 
3. Function spaces for decoupling. 2023, 41 pages. Available here. By A. Hassell, P. Portal, J. Rozendaal and P.-L. Yung.
4. Local smoothing and Hardy spaces for Fourier integral operators on manifolds. J. Funct. Anal. 286 (2024), no. 2, Paper No. 110221, 72 pp. By N. Liu, J. Rozendaal, L. Song and L. Yan.

Presentations:

• Analysis Seminar. Delft University of Technology, Netherlands. April 2024. By J. Rozendaal. 
• Geometric Function and Mapping Theory seminar. IMPAN. April 2024. By A. Ghosh.
• Harmonic Analysis on Manifolds, conference. Loughborough, United Kingdom. April 2024. By J. Rozendaal.
• Dynamics and Thermodynamics of Large Interacting Systems, conference. IMPAN, March 2024. By J. Rozendaal.
• US-Poland-Ukraine seminar on wave equations and related matters. Video presentation. March 2024. By J. Rozendaal.
• Harmonic Analysis and Orthogonal Expansions. University of Wrocław, Poland. March 2024. By A. Ghosh. 
• Leibniz University Hannover, Germany. November 2023. By J. Rozendaal.
• Geometric Function and Mapping Theory seminar. IMPAN. November 2023. By J. Rozendaal.
• Sun Yat-Sen University, China. October 2023. By J. Rozendaal.
• Kiel University, Germany. April 2023. By J. Rozendaal.
• AustMS Annual Meeting 2022, conference. Sydney, Australia. December 2022. By J. Rozendaal.
• Analysis and PDE seminar. Australian National University, Australia. November 2022. By J. Rozendaal.
• Analysis seminar. Monash University, Australia. November 2022. By J. Rozendaal.
• Analysis seminar. Macquarie University, Australia. November 2022. By J. Rozendaal.

Travels:

• Delft University of Technology. Netherlands. April 2024. By J. Rozendaal.
• Harmonic Analysis on Manifolds, conference. Loughborough, United Kingdom. 2-5 April 2024. By J. Rozendaal.
• University of Wrocław, Poland. 5-7 March 2024. By A. Ghosh. 
• Leibniz University Hannover, Germany. 19-22 November 2023. By J. Rozendaal.
• Sun Yat-Sen University, China. 4-17 October 2023. By J. Rozendaal.
• Kiel University, Germany. 17-21 April 2023. By J. Rozendaal.
• AustMS Annual Meeting 2022, conference. Sydney, Australia. 6-9 December 2022. By J. Rozendaal. 
• Australian National University, Australia. 13 November to 4 December 2022. By J. Rozendaal.
• Sydney, Canberra and Melbourne, Australia. 28 October to 12 November 2022. By J. Rozendaal.