2022/01/30 by Duván Cardona, Michael Ruzhansky, Cardona, Duván +1
Mathematics · #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Representation Theory (math.RT) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2201.12883
openalex publication_date 2022/01/30 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Stein for the boundedness of oscillating convolution operators. Kernel criteria are presented in terms of a fixed sub-Riemannian structure on the group induced by a sub-Laplacian associated to a Hörmander system of vector fields. In the case where the group is graded, kernel criteria are presented in terms of the Fourier analysis associated to an arbitrary Rockland operator.