Alessio Martini

e-mail address: a DOT martini AT bham DOT ac DOT uk
member of the Mathematical Analysis Research Group at the University of Birmingham


  • (with V. Casarino and P. Ciatti) Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators. International Mathematics Research Notices 2021 (online). doi:10.1093/imrn/rnab007
  • (with M. Vallarino) Riesz transforms on solvable extensions of stratified groups. Studia Mathematica 259(2):175-200, 2021. doi:10.4064/sm190927-4-1
  • (with A. D. Horwich) Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups. Journal of the London Mathematical Society 103(3):1066-1119, 2021. doi:10.1112/jlms.12401
  • (with G. M. Dall'Ara) A robust approach to sharp multiplier theorems for Grushin operators. Transactions of the American Mathematical Society 373(11):7533-7574, 2020. doi:10.1090/tran/7844
  • (with S. Meda and M. Vallarino) A family of Hardy type spaces on nondoubling manifolds. Annali di Matematica Pura ed Applicata 199:2061-2085, 2020. doi:10.1007/s10231-020-00956-9
  • (with J. Ahrens, M. G. Cowling, and D. Müller) Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres. Mathematische Zeitschrift 294(3-4):1659-1686, 2020. doi:10.1007/s00209-019-02313-w
  • (with A. Ottazzi and M. Vallarino) A multiplier theorem for sub-Laplacians with drift on Lie groups. Revista Matemática Iberoamericana 35(5):1501-1534, 2019. doi:10.4171/rmi/1090
  • (with M. G. Cowling, D. Müller, and J. Parcet) The Hausdorff-Young inequality on Lie groups. Mathematische Annalen 375(1-2):93-131, 2019. doi:10.1007/s00208-018-01799-9
  • (with F. Ricci and L. Tolomeo) Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth. Journal of Functional Analysis 277(6):1603-1638, 2019. doi:10.1016/j.jfa.2019.05.024
  • (with V. Casarino and P. Ciatti) From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere. Advances in Mathematics 350:816-859, 2019. doi:10.1016/j.aim.2019.05.003
  • (with A. Ottazzi and M. Vallarino) Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups. Journal d'Analyse Mathématique 136(1):357-397, 2018. doi:10.1007/s11854-018-0063-6
  • (with V. Casarino, M. G. Cowling, and A. Sikora) Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn. Journal of Geometric Analysis 27(4):3302-3338, 2017. doi:10.1007/s12220-017-9806-3
  • Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres. Mathematische Zeitschrift 286(3-4):1539-1574, 2017. doi:10.1007/s00209-016-1813-8
  • (with D. Müller) Spectral multipliers on 2-step groups: topological versus homogeneous dimension. Geometric and Functional Analysis 26(2):680-702, 2016. doi:10.1007/s00039-016-0365-8
  • Spectral multipliers on Heisenberg-Reiter and related groups. Annali di Matematica Pura ed Applicata 194(4):1135-1155, 2015. doi:10.1007/s10231-014-0414-6
  • (with D. Müller) A sharp multiplier theorem for Grushin operators in arbitrary dimensions. Revista Matemática Iberoamericana 30(4):1265-1280, 2014. doi:10.4171/rmi/814
  • (with D. Müller) Spectral multiplier theorems of Euclidean type on new classes of two-step stratified groups. Proceedings of the London Mathematical Society 109(5):1229-1263, 2014. doi:10.1112/plms/pdu033
  • (with D. Müller) Lp spectral multipliers on the free group N3,2. Studia Mathematica 217(1):41-55, 2013. doi:10.4064/sm217-1-3
  • (with M. G. Cowling) Sub-Finsler geometry and finite propagation speed. In Trends in Harmonic Analysis (M. A. Picardello ed.), Springer 2013, pp. 147-205. doi:10.1007/978-88-470-2853-1_8
  • (with A. Sikora) Weighted Plancherel estimates and sharp spectral multipliers for the Grushin operators. Mathematical Research Letters 19(5):1075-1088, 2012. doi:10.4310/MRL.2012.v19.n5.a9
  • Analysis of joint spectral multipliers on Lie groups of polynomial growth. Annales de l'Institut Fourier 62(4):1215-1263, 2012. doi:10.5802/aif.2721
  • Spectral theory for commutative algebras of differential operators on Lie groups. Journal of Functional Analysis 260(9):2767-2814, 2011. doi:10.1016/j.jfa.2011.01.008
  • Generalized uncertainty inequalities. Mathematische Zeitschrift 265(4):831-848, 2010. doi:10.1007/s00209-009-0544-5


  • (with S. Meda and M. Vallarino) Maximal characterisation of local Hardy spaces on locally doubling manifolds, 2021. arXiv:2103.03016
  • (with V. Casarino and P. Ciatti) Uniform pointwise estimates for ultraspherical polynomials, 2020. arXiv:2009.02323
  • (with D. Müller and S. Nicolussi Golo) Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type, 2018. arXiv:1812.02671

Book editing

PhD thesis

  • Algebras of differential operators on Lie groups and spectral multipliers, Scuola Normale Superiore (Pisa, Italy), 2010. arXiv:1007.1119