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Research

Versions here may slightly differ from the published ones. Most of my papers are also available in arXiv.
  1. O. Saari, Y. Sun, H.-Y. Wang and Y. Wei, A duality approach to gradient Hölder estimates for linear divergence form elliptic equations, submitted.
  2. K. Myyryläinen, T. Oikari and O. Saari, Domains with globally exponentially integrable parabolic forward-in-time BMO, submitted.
  3. S. Bortz, M. Egert and O. Saari, A stability result for parabolic measures of operators with singular drifts, submitted.
  4. O. Saari, H.-Y. Wang and Y. Wei, Sparse gradient bounds for divergence form elliptic equations, J. Differential Equations 413 (2024), 606-631.
  5. M. Fraccaroli, O. Saari and C. Thiele, Uniform bounds for bilinear symbols with linear K-quasiconformally embedded singularity, Anal. PDE 18 (2025), No. 9, 2293-2323.
  6. M. Fraccaroli, O. Saari and C. Thiele, Phase space localizing operators, submitted.
  7. D. Beltran and O. Saari, Lp-Lq local smoothing estimates for the wave equation via k-broad Fourier restriction, J. Fourier Anal. Appl. 28 (2022), Paper No. 76.
  8. S. Bortz, M. Egert and O. Saari, Carleson Conditions for Weights: The quantitative small constant case, Nonlinear Anal. 257 (2025), 113802.
  9. O. Saari and S. Schwarzacher, Construction of a right inverse for the divergence in non-cylindrical time dependent domains, Ann. PDE. 9 (2023), Paper No. 8.
  10. O. Saari and C. Thiele, Paraproducts for bilinear multipliers associated with convex sets, Math. Ann. 385 (2023), 2013–2036.
  11. S. Bortz, M. Egert and O. Saari, Note on time-regularity for weak solutions to parabolic systems of p-Laplace type, Proc. Amer. Math. Soc. 149 (2021), 1677-1685.
  12. S. Bortz, M. Egert and O. Saari, Sobolev contractivity of gradient flow maximal functions, Adv. Calc. Var. 17 (2024), 1487-1505.
  13. O. Saari and S. Schwarzacher, A reverse Hölder inequality for the gradient of solutions to Trudinger's equation, NoDEA Nonlinear Differential Equations Appl. 29 (2022), Paper No. 24.
  14. J.P. Ramos, O. Saari and J. Weigt, Weak differentiability for fractional maximal functions of general Lp functions on domains, Adv. Math. 368 (2020), 107144.
  15. M. Akman, J. Lewis, O. Saari and A. Vogel, The Brunn-Minkowski inequality and a Minkowski problem for A-harmonic Green's function, Adv. Calc. Var. 14 (2021), 247-302.
  16. D. Beltran, J.P. Ramos and O. Saari, Regularity of fractional maximal functions through Fourier multipliers, J. Funct. Anal. 276 (2019), 1875-1892.
  17. C. Pérez, T. Picon, O. Saari and M. Sousa, Regularity of maximal functions on Hardy-Sobolev spaces, Bull. London Math. Soc. 50 (2018), 1007-1015.
  18. P. Auscher, S. Bortz, M. Egert and O. Saari, Non-local self-improving properties: a functional analytic approach, Tunis. J. Math. 1 (2019), 151-183.
  19. P. Auscher, S. Bortz, M. Egert and O. Saari, Non-local Gehring lemmas in spaces of homogeneous type and applications, J. Geom. Anal. 30 (2020), 3760-3805.
  20. P. Auscher, S. Bortz, M. Egert and O. Saari, On regularity of weak solutions to linear parabolic systems with measurable coefficients, J. Math. Pures Appl. 121 (2019), 216-243.
  21. O. Saari and C. Thiele, Lipschitz linearization of the maximal hyperbolic cross multiplier, J. Fourier Anal. Appl. 25 (2019), 167-183.
  22. O. Saari, Poincaré inequalities for the maximal function, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 19 (2019), 1065-1083.
  23. O. Saari, Parabolic BMO and the forward-in-time maximal operator, Ann. Mat. Pura Appl. (4) 197 (2018), 1477-1497.
  24. P.A. Hagelstein, I. Parissis and O. Saari, Sharp inequalities for one-sided Muckenhoupt weights, Collect. Math. 69 (2018), 151-161.
  25. B. Avelin and O. Saari, Characterizations of interior polar sets for the degenerate p-parabolic equation, J. Evol. Equ. 17 (2017), 827-848.
  26. J. Kinnunen and O. Saari, On weights satisfying parabolic Muckenhoupt conditions, Nonlinear Anal. 131 (2016), 289-299.
  27. R. Korte, N. Marola and O. Saari, Homeomorphisms of the Heisenberg group preserving BMO, Arch. Math. (Basel) 106 (2016), 175-182.
  28. J. Kinnunen and O. Saari, Parabolic weighted norm inequalities and partial differential equations, Anal. PDE 9 (2016), 1711-1736.
  29. O. Saari, Parabolic BMO and global integrability of supersolutions to doubly nonlinear parabolic equations, Rev. Mat. Iberoam. 32 (2016), 1001-1018.
  30. N. Marola and O. Saari, Local to global results for spaces of BMO type, Math. Z. 282 (2016), 473-484.