Mathematisches Institut |

Endenicher Allee 60 |

D - 53115 Bonn |

Office: 3.012 |

Tel: +49 228 73-62338 |

E-mail: saari at math dot uni-bonn dot de |

I am post-doc at the University of Bonn. I obtained D.Sc. (Tech.) in Mathematics at Aalto University (Finland) under supervision of Juha Kinnunen. My research interests include harmonic analysis, PDE and their interaction. In particular, I have been studying parabolic PDE, weighted norm inequalities and maximal functions.

- D. Beltran, J.P. Ramos and O. Saari, Regularity of fractional maximal functions through Fourier multipliers, submitted.
- C. Pérez, T. Picon, O. Saari and M. Sousa, Regularity of maximal functions on Hardy-Sobolev spaces, to apppear in Bull. Lond. Math. Soc.
- P. Auscher, S. Bortz, M. Egert and O. Saari, Non-local self-improving properties: a functional analytic approach, Tunisian Journal of Mathematics 1 (2019), 151-183.
- P. Auscher, S. Bortz, M. Egert and O. Saari, Non-local Gehring lemmas in spaces of homogeneous type and applications, submitted.
- P. Auscher, S. Bortz, M. Egert and O. Saari, On regularity of weak solutions to linear parabolic systems with measurable coefficients, to appear in J. Math. Pures Appl.
- O. Saari and C. Thiele, Lipschitz linearization of the maximal hyperbolic cross multiplier, J. Fourier Anal. Appl. (link).
- O. Saari, Poincaré inequalities for the maximal function, to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5).
- O. Saari, Parabolic BMO and the forward-in-time maximal operator, Ann. Mat. Pura Appl. (4) (link).
- P.A. Hagelstein, I. Parissis and O. Saari, Sharp inequalities for one-sided Muckenhoupt weights, Collect. Math. 69 (2018), 151-161.
- B. Avelin and O. Saari, Characterizations of interior polar sets for the degenerate p-parabolic equation, J. Evol. Equ. 17 (2017), 827-848.
- 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.

- On endpoint regularity of maximal functions,

ICMAT (5.6.2018) - Spherical means and derivatives of fractional maximal
functions,

ICMAT (Workshop on Real Harmonic Analysis etc. 29.5.2018) - Functional analytic approach to non-local self-improving properties,

University of Bonn (18.5.2018), Institut Mittag-Leffler (Workshop on Nonlinear Parabolic PDEs 13.6.2018) - Endpoint bounds for derivative of fractional maximal
function,

BCAM (22.3.2018) - Hölder continuity in time for linear parabolic systems,

University of Eastern Finland (Finnish mathematical days 5.1.2018) - Muckenhoupt weights and their dynamical counterpart,

MSRI (7.4.2017) - Regularity of the maximal function and Poincaré inequalities,

University of Bonn (11.11.2016), BCAM (27.6.2017). - 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), BCAM (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).