Refereed journal articles

  1. T. Hytönen, K. Li, H. Martikainen, E. Vuorinen, Multiresolution analysis and Zygmund dilations, American Journal of Mathematics, to appear (arXiv:2203.15777, 2022).
  2. T. Hytönen, K. Li, H. Martikainen, E. Vuorinen, Exotic Calderón-Zygmund operators, The Journal of Geometric Analysis 33 (2023), article number 157, https://doi.org/10.1007/s12220-023-01216-x.
  3. E. Airta, K. Li, H. Martikainen, Two-weight inequalities for multilinear commutators in product spaces, Potential Analysis (2022), https://doi.org/10.1007/s11118-022-10032-x.
  4. E. Airta, H. Martikainen, E. Vuorinen, UMD-extensions of Calderón–Zygmund operators with mild kernel regularity, Journal of Fourier Analysis and Applications 28 (2022), article number 64, https://doi.org/10.1007/s00041-022-09960-4. (Part 1/2 of arXiv:2006.05807)
  5. E. Airta, H. Martikainen, E. Vuorinen, Product space singular integrals with mild kernel regularity, The Journal of Geometric Analysis 32 (2022), article number 24, https://doi.org/10.1007/s12220-021-00757-3. (Part 2/2 of arXiv:2006.05807)
  6. K. Li, H. Martikainen, E. Vuorinen, Genuinely multilinear weighted estimates for singular integrals in product spaces, Advances in Mathematics 393 (2021) 108099, https://doi.org/10.1016/j.aim.2021.108099.
  7. E. Airta, T. Hytönen, K. Li, H. Martikainen, T. Oikari, Off-diagonal estimates for bi-commutators, International Mathematics Research Notices 2022 (23) (2022) 18766–18832, https://doi.org/10.1093/imrn/rnab239.
  8. F. Di Plinio, K. Li, H. Martikainen, E. Vuorinen, Multilinear singular integrals on non-commutative Lp spaces, Mathematische Annalen 378 (2020) 1371–1414, https://doi.org/10.1007/s00208-020-02068-4.
  9. F. Di Plinio, K. Li, H. Martikainen, E. Vuorinen, Banach-valued multilinear singular integrals with modulation invariance, International Mathematics Research Notices 2022 (7) (2022) 5256–5319, https://doi.org/10.1093/imrn/rnaa234.
  10. F. Di Plinio, K. Li, H. Martikainen, E. Vuorinen, Multilinear operator-valued Calderón–Zygmund theory, Journal of Functional Analysis 279 (8) (2020) 108666, https://doi.org/10.1016/j.jfa.2020.108666.
  11. E. Airta, K. Li, H. Martikainen, E. Vuorinen, Some new weighted estimates on product spaces, Indiana University Mathematics Journal 71 (1) (2022) 37–63, https://doi.org/10.1512/iumj.2022.71.8807.
  12. K. Li, J. M. Martell, H. Martikainen, S. Ombrosi, E. Vuorinen, End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications, Transactions of the American Mathematical Society 374 (1) (2021) 97–135, https://doi.org/10.1090/tran/8172.
  13. K. Li, H. Martikainen, E. Vuorinen, Bilinear Calderón–Zygmund theory on product spaces, Journal de Mathématiques Pures et Appliquées 138 (2020) 356–412, https://doi.org/10.1016/j.matpur.2019.10.007.
  14. T. Hytönen, H. Martikainen, E. Vuorinen, Multi-parameter estimates via operator-valued shifts, Proceedings of the London Mathematical Society 119 (6) (2019) 1560–1597, https://doi.org/10.1112/plms.12279.
  15. K. Li, H. Martikainen, E. Vuorinen, Bloom type upper bounds in the product BMO setting, The Journal of Geometric Analysis 30 (2020) 3181–3203, https://doi.org/10.1007/s12220-019-00194-3.
  16. K. Li, H. Martikainen, E. Vuorinen, Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators, International Mathematics Research Notices 2021 (11) (2021) 8153–8187, https://doi.org/10.1093/imrn/rnz072.
  17. H. Martikainen, M. Mourgoglou, E. Vuorinen, A new approach to non-homogeneous local Tb theorems, Journal d’Analyse Mathématique 143 (2021) 95–121, https://doi.org/10.1007/s11854-021-0147-6.
  18. H. Martikainen, E. Vuorinen, Dyadic-probabilistic methods in bilinear analysis, Memoirs of the American Mathematical Society 274 (1344) (2021), https://doi.org/10.1090/memo/1344.
  19. K. Li, H. Martikainen, Y. Ou, E. Vuorinen, Bilinear representation theorem, Transactions of the American Mathematical Society 371 (6) (2019) 4193–4214, https://doi.org/10.1090/tran/7505.
  20. H. Martikainen, M. Mourgoglou, X. Tolsa, Improved Cotlar’s inequality in the context of local Tb theorems, Journal of Functional Analysis 274 (2018) 1255–1275, https://doi.org/10.1016/j.jfa.2017.12.013.
  21. H. Martikainen, T. Orponen, Boundedness of the density normalised Jones’ square function does not imply 1-rectifiability, Journal de Mathématiques Pures et Appliquées (2018) 71–92, https://doi.org/10.1016/j.matpur.2017.07.009.
  22. H. Martikainen, M. Mourgoglou, E. Vuorinen, Non-homogeneous square functions on general sets: suppression and big pieces methods, The Journal of Geometric Analysis 27 (4) (2017) 3176–3227, http://dx.doi.org/10.1007/s12220-017-9801-8.
  23. H. Martikainen, M. Mourgoglou, Note about square function estimates and uniformly rectifiable measures, Proceedings of the American Mathematical Society 144 (8) (2016) 3455–3463, http://dx.doi.org/10.1090/proc/13128.
  24. H. Martikainen, T. Orponen, Characterising the big pieces of Lipschitz graphs property using projections, Journal of the European Mathematical Society 20 (5) (2018) 1055–1073, https://doi.org/10.4171/JEMS/782.
  25. H. Martikainen, T. Orponen, Some obstacles in characterising the boundedness of bi-parameter singular integrals, Mathematische Zeitschrift 282 (2016) 535–545, http://dx.doi.org/10.1007/s00209-015-1552-2.
  26. H. Martikainen, M. Mourgoglou, Boundedness of non-homogeneous square functions and Lq type testing conditions with q in (1,2), Mathematical Research Letters 22 (5) (2015) 1417–1457, http://dx.doi.org/10.4310/MRL.2015.v22.n5.a8.
  27. M. Lacey, H. Martikainen, Local Tb theorem with L2 testing conditions and general measures: Calderón–Zygmund operators, Annales scientifiques de l’École normale supérieure 49 (1) (2016) 57–86, https://doi.org/10.24033/asens.2276.
  28. M. Lacey, H. Martikainen, Local Tb theorem with L2 testing conditions and general measures: Square functions, Journal d’Analyse Mathématique 133 (1) (2017) 71–89, http://dx.doi.org/10.1007/s11854-017-0028-1.
  29. H. Martikainen, M. Mourgoglou, T. Orponen, Square functions with general measures II, Indiana University Mathematics Journal 63 (5) (2014) 1249–1279, http://dx.doi.org/10.1512/iumj.2014.63.5379.
  30. H. Martikainen, Boundedness of a class of bi-parameter square functions in the upper half-space, Journal of Functional Analysis 267 (10) (2014) 3580–3597, http://dx.doi.org/10.1016/j.jfa.2014.09.006.
  31. H. Martikainen, M. Mourgoglou, Square functions with general measures, Proceedings of the American Mathematical Society 142 (11) (2014) 3923–3931, http://dx.doi.org/10.1090/S0002-9939-2014-12145-9.
  32. T. Hytönen, H. Martikainen, Non-homogeneous T1 theorem for bi-parameter singular integrals, Advances in Mathematics 261 (2014) 220–273, http://dx.doi.org/10.1016/j.aim.2014.02.011.
  33. H. Martikainen, Representation of bi-parameter singular integrals by dyadic operators, Advances in Mathematics 229 (3) (2012) 1734–1761, http://dx.doi.org/10.1016/j.aim.2011.12.019.
  34. T. Hytönen, M. Lacey, H. Martikainen, T. Orponen, M. C. Reguera, E. Sawyer, I. Uriarte–Tuero, Weak and strong type estimates for maximal truncations of Calderón–Zygmund operators on Ap weighted spaces, Journal d’Analyse Mathématique 118 (1) (2012) 177–220, http://dx.doi.org/10.1007/s11854-012-0033-3.
  35. T. Hytönen, H. Martikainen, On general local Tb theorems, Transactions of the American Mathematical Society 364 (9) (2012) 4819–4846, http://dx.doi.org/10.1090/S0002-9947-2012-05599-1.
  36. H. Martikainen, Vector-valued non-homogeneous Tb theorem on metric measure spaces, Revista Matemática Iberoamericana 28 (4) (2012) 961–998, http://dx.doi.org/10.4171/RMI/699.
  37. T. Hytönen, H. Martikainen, Non-homogeneous Tb theorem and random dyadic cubes on metric measure spaces, The Journal of Geometric Analysis 22 (4) (2012) 1071–1107, http://dx.doi.org/10.1007/s12220-011-9230-z.

Preprints

  1. E. Airta, K. Li, H. Martikainen, Zygmund dilations: bilinear analysis and commutator estimates, preprint, arXiv:2301.13655, 2023.

PhD thesis

  • H. Martikainen, Global, local and vector-valued Tb theorems on non-homogeneous metric spaces, University of Helsinki, Faculty of Science, Department of Mathematics and Statistics (2011), http://urn.fi/URN:ISBN:978-952-10-7366-3.