Harmonic analysis on Lie groups

Members:
D. Müller, Christian-Albrechts-Universität, Kiel
Alexander Nagel, University of Wisconsin, Madison
Marco M. Peloso, Politecnico di Torino
Fulvio Ricci, Scuola Normale Superiore, Pisa
Elias M. Stein, Princeton University
Steven Wainger, University of Wisconsin, Madison

Research interests:
Analysis of operators on Lie groups associated to generating systems of invariant vector fields, and realted problems

Current research projects:
Singular integrals of product type on Lie groups and manifolds, defined in terms of the flow generated by systems of vector fields satisfying the Hörmander condition (A. Nagel, F. Ricci, E.M. Stein, S. Wainger).
Spectral multipliers of the left-invariant Laplacians and sub-Laplacians acting of differential forms on the Heisenberg group (D. Müller, M.M. Peloso, F. Ricci)

Related publications:
D. Müller, E. M. Stein, On spectral multipliers for Heisenberg and related groups, J. Math. Pures Appl. 73 (1994), 413-440.
D. Müller, F. Ricci, E.M. Stein, Marcinkiewicz multipliers and multi-parameter structure on Heisenberg(-type) groups, I, Invent. Math. 119 (1995), 199-233.
D. Müller, F. Ricci, E.M. Stein, Marcinkiewicz multipliers and multi-parameter structure on Heisenberg(-type) groups, II, Math. Zeitschr. 221 (1996), 267-291.
M. Christ, A. Nagel, E.M. Stein, S. Wainger, Singular and maximal Radon transforms: analysis anf geometry, Ann. Math. 150 (1999), 489-577.
A. Nagel, F. Ricci, E.M. Stein, Singular integrals with flag kernels and analysis on quadratic manifolds, J. Funct. Anal. 181 (2001), 29-118.
A. Nagel, E.M. Stein, On the product theory of singular integrals, Rev Mat. Iberoam. 20 (2004), 531-561.
D. Müller, M. Peloso, F. Ricci, Lp-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group, preprint.