Olli Saari's Homepage
I received my PhD from Aalto University in April 2016. My advisor was Juha Kinnunen, the research group "Nonlinear Partial Differential Equations". During the spring term 2017, I am a postdoctoral fellow at the MSRI in Berkeley.
My research is in the interface of harmonic analysis and PDE. My doctoral thesis was about parabolic PDE and weighted norm inequalities. In addition to that, I have studied potential theory of the p-parabolic equation and topics related to maximal functions and spaces of BMO type.
harmonic analysis, partial differential equations
Doctoral Thesis (2016), Weights arising from parabolic partial differential equations, Advisor: Juha Kinnunen.
- O. Saari and C. Thiele, Lipschitz linearization of the maximal hyperbolic cross multiplier, submitted.
- O. Saari, Poincaré inequalities for the maximal function, submitted.
- O. Saari, Parabolic BMO and the forward-in-time maximal operator, submitted.
- P. Hagelstein, I. Parissis and O. Saari, Sharp inequalities for one-sided Muckenhoupt weights, submitted.
- B. Avelin and O. Saari, Characterizations of interior polar sets for the degenerate p-parabolic equation, to appear in J. Evol. Equ. (link).
- J. Kinnunen and O. Saari, On weights satisfying parabolic Muckenhoupt conditions, Nonlinear Anal. 131 (2016), 289-299.
- R. Korte, N. Marola and O. Saari, Homeomorphisms of the Heisenberg group preserving BMO, Arch. Math. (Basel) 106 (2016), 175-182.
- J. Kinnunen and O. Saari, Parabolic weighted norm inequalities and partial differential equations, Anal. PDE. 9 (2016), 1711-1736.
- O. Saari, Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations, Rev. Mat. Iberoam. 32 (2016), 1001-1018.
- N. Marola and O. Saari, Local to global results for spaces of BMO type, Math. Z. 282 (2016), 473-484.
Master's Thesis (2013), Lokaalista globaaliin -tuloksia John-Nirenberg-epäyhtälöille, in Finnish.
- Regularity of the maximal function and Poincaré inequalities,
University of Bonn (11.11.2016).
- Parabolic BMO and the forward-in-time maximal operator,
University of Helsinki (The conference Singular integrals and partial differential equations 26.5.2016), El Escorial (15.6.2016).
- Exceptional sets for the p-parabolic equation,
University of Helsinki (22.1.2016), Basque Center for Applied Mathematics (Summer School on Harmonic analysis and PDE 7.7.2016).
- Weights from parabolic PDE,
Aalto University (The conference HAPDE2015 9.6.2015), University of the Basque Country (2.10.2015), University of Bonn (6.11.2015), University of Málaga (27.11.2015),
Universitat Autònoma de Barcelona (14.12.2015).