Alessio Martini

Professor of Mathematical Analysis at Politecnico di Torino (Italy)
e-mail address: alessio DOT martini AT polito DOT it

Publications

- (with F. Santagati and M. Vallarino) Heat kernel and Riesz transform for the flow Laplacian on homogeneous trees. In (New Trends in) Complex and Fourier Analysis (N. Arcozzi, M.M. Peloso and A. Tabacco eds.), Springer INdAM Series, Springer (to appear). arXiv:2210.07148
- (with F. Santagati, A. Tabacco and M. Vallarino) Riesz transform and spectral multipliers for the flow Laplacian on nonhomogeneous trees. Revista Matemática Iberoamericana (online 2025). doi:10.4171/rmi/1578
- (with P. Plewa) A sharp multiplier theorem for solvable extensions of Heisenberg and related groups. Annali di Matematica Pura ed Applicata 203(3):1361-1408, 2024. doi: 10.1007/s10231-023-01405-z
- (with S. Meda, M. Vallarino and G. Veronelli) Inclusions and noninclusions of Hardy type spaces on certain nondoubling manifolds, Journal of Functional Analysis 286(3):110240, 2024 (39 pp.). doi:10.1016/j.jfa.2023.110240
- (with G. M. Dall'Ara) An optimal multiplier theorem for Grushin operators in the plane, I. Revista Matemática Iberoamericana 39(3):897-974, 2023. doi:10.4171/rmi/1374
- Riesz transforms on ax + b groups. Journal of Geometric Analysis 33(7):222, 2023 (53 pp.). doi:10.1007/s12220-023-01289-8
- (with D. Müller and S. Nicolussi Golo) Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type. Journal of the European Mathematical Society 25(3):785-843, 2023. doi:10.4171/JEMS/1191
- (with M. Levi, F. Santagati, A. Tabacco and M. Vallarino) Riesz transform for a flow Laplacian on homogeneous trees. Journal of Fourier Analysis and Applications 29(2):15, 2023 (29 pp.). doi:10.1007/s00041-023-09999-x
- (with V. Casarino and P. Ciatti) Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators. International Mathematics Research Notices 2022(12):9209-9274, 2022. doi:10.1093/imrn/rnab007
- (with G. M. Dall'Ara) An optimal multiplier theorem for Grushin operators in the plane, II. Journal of Fourier Analysis and Applications 28(2):32, 2022 (29 pp.). doi:10.1007/s00041-022-09931-9
- (with S. Meda and M. Vallarino) Maximal characterisation of local Hardy spaces on locally doubling manifolds. Mathematische Zeitschrift 300(2):1705-1739, 2022. doi:10.1007/s00209-021-02856-x
- (with V. Casarino and P. Ciatti) Uniform pointwise estimates for ultraspherical polynomials. Comptes Rendus Mathématique 359(10):1239-1250, 2021. doi:10.5802/crmath.255
- (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

Preprints

- (with P. Plewa) Lp-boundedness of Riesz transforms on solvable extensions of Carnot groups, 2024 (27 pp.). arXiv:2409.13233
- (with P. Plewa) Singular integrals on ax + b hypergroups and an operator-valued spectral multiplier theorem, 2024 (64 pp.). arXiv:2409.12833
- (with D. Müller) An FIO-based approach to Lp-bounds for the wave equation on 2-step Carnot groups: the case of Métivier groups, 2024 (92 pp.). arXiv:2406.04315

Book editing

- (with P. Ciatti) Geometric Aspects of Harmonic Analysis, Springer INdAM Series, vol. 45, Springer, 2021. doi:10.1007/978-3-030-72058-2

PhD thesis

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

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