Associate professor in Geometry
Università degli Studi di Padova
e-mail: valentina.casarino@unipd.it
Tel. +39-0444-998708
Skype: vcasarino
Research interests
Harmonic analysis on spheres, even complex and quaternionic; spectral properties of differential operators on spaces of differential forms
Gaussian harmonic analysis
Nilpotent Lie groups; restriction properties of spectral projections arising from the spectral decomposition of Laplacians and subLaplacians.
Recent publications
R. Bramati e V. Casarino, Lower bounds for spherical harmonics on the octonionic sphere, RIMS Kokyuroku, "Recent Development on Representation Theory, Lie theory and Related Areas".
T. Bruno, V. Casarino, P. Ciatti e P. Sjoegren, Boundedness properties of the maximal ope rator in a nonsymmetric inverse Gaussian setting, Potential Anal 63, 2077–2098 (2025), https://doi.org/10.1007/s11118-025-10233-0
V. Casarino e P. Ciatti, Some mixed norm bounds for the spectral projections of the Heisenberg sublaplacian, in “Symmetry in Geometry and Analysis - Festschrift for Toshiyuki Kobayashi, Progress in Mathematics”, Springer-Birkh¨auser (2025).
V. Casarino, P. Ciatti e P. Sjögren, Variational inequalities for the Ornstein--Uhlenbeck semigroup: the higher--dimensional case, J. Geom. Anal. (2025), 35, https://doi.org/10.1007/s12220-024-01859-4.
V. Casarino, P. Ciatti e P. Sjögren, Spectral multipliers in a general Gaussian setting, in corso di stampa su Ann. Sc. Norm. Super. Pisa Cl. Sci., https://doi.org/10.2422/2036-2145.202311_014.
V. Casarino, P. Ciatti and P. Sjögren, On the variation operator for the Ornstein--Uhlenbeck semigroup in dimension one, Annali di Matematica Pura e Applicata 203, 205-219 (2024), https://doi.org/10.1007/s10231-023-01358-3
V. Casarino, P. Ciatti e P. Sjögren, On the maximal operator of a general Ornstein--Uhlenbeck semigroup, Math. Z. , 301, (2022), pp.2393–2413, https://doi.org/10.1007/s00209-022-02986-w.
V. Casarino, P. Ciatti e A. Martini, Uniform pointwise estimates for ultraspherical polynomials, Comptes Rendus. Mathématique, 359 (2021) no. 10, pp. 1239–1250, https://doi.org/10.5802/crmath.255
V. Casarino, P. Ciatti e P. Sjögren, On the orthogonality of generalized eigenspaces for the Ornstein--Uhlenbeck operator, Archiv der Matematik 117, 547–556 (2021). https://doi.org/10.1007/s00013-021-01637-6
V. Casarino, P. Ciatti and A .Martini, Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators, International Mathematics Research Notices (to appear), arXiv:2009.02916.
V. Casarino, P. Ciatti e P. Sjögren, Riesz transforms of a general Ornstein--Uhlenbeck semigroup, Calculus of Variations and Partial Differential Equations 60, 135 (2021). https://doi.org/10.1007/s00526-021-01988-6.
V. Casarino, P. Ciatti and P. Sjögren, The maximal operator of a normal Ornstein-Uhlenbeck semigroup is of weak type (1,1), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXI (2020), 385-410, DOI : 10.2422/2036-2145.201805_012, arXiv:1705.00833,
V. Casarino, P. Ciatti and A. Martini, From refined estimates for the spherical harmonics to a sharp multiplier theorem on the Grushin sphere, Advances in Mathematics 350 (2019), 816-859. doi:10.1016/j.aim.2019.05.003, arXiv:1705.07068.
R. Bramati, V. Casarino e P. Ciatti, On the norms of quaternionic harmonic projection operators, C. R. Acad. Sci. Paris, Ser. I, 356 (2018), 482-488, DOI 10.1016/j.crma.2018.03.011
V. Casarino, M.G. Cowling, A. Martini e A. Sikora, Spectral multipliers for the Kohn Laplacian on forms on the sphere in C^n, arXiv:1501.02321v1, Journal of Geometric Analysis 27 (2017), 3302-3338, DOI 10.1007/s12220-017-9806-3.
V. Casarino e P. Ciatti, L^p joint eigenfunction bounds on quaternionic spheres, J.Fourier Anal. Appl. 23 (2017), 886-918, DOI 10.1007/s00041-016-9506-6.
V. Casarino, Some remarks on harmonic projection operators on spheres, Bruno Pini Mathematical Analysis Seminar (2016), DOI: 10.6092/issn.2240-2829/6685.
V. Casarino and M. Peloso, Strichartz estimates and the nonlinear Schroedinger equation for the sublaplacian on complex spheres,
Trans. Amer. Math. Soc. 367 (2015), 2631-2664.
V. Casarino and P. Ciatti, A Restriction Theorem for Metivier Groups, Advances in Mathematics 245 (2013), 52-77.
V. Casarino and P. Ciatti, Restriction estimates for the full Laplacian on Metivier Groups, Rend. Lincei Mat. Appl. 24
(2013), 165-179.
V. Casarino, P. Ciatti and S. Secco, Product structures and fractional integration along curves in the space, DCDS (s), 6(3), (2013),
p.619-635,
V. Casarino, P. Ciatti and S. Secco, Product kernels adapted to curves in the space, Revista Matematica Iberoamericana 27 (2011), 1023-1057.
V. Casarino and M. Peloso, L^p -summability of Riesz means for the sublaplacian on complex spheres, Journal of the London Mathematical Society 83 (2011), 137-152.
V. Casarino and P. Ciatti, Transferring L^p eigenfunction bounds from S^{2n+1} to h^n, Studia Mathematica, 194 (2009), 23-42.
V. Casarino, Two-parameter estimates for joint spectral projections on complex spheres, Math. Z., 261 (2009), 245-259.