Next Monday May 2, Duvan Cardona Sanchez will give a talk organized by DeustoCCM – Chair of Computational Mathematics on:
“Fefferman-Stein Theory for Oscillating Singular Integrals”

Slides

Abstract. Oscillating Fourier multipliers on the torus and on Rⁿ play a fundamental role in analysis and PDE and in the setting of Lie groups are still a subject of intensive research. The classical results by Fefferman and Stein in this direction (published between 1970 and 1972 in Acta Math.) have consolidated a fundamental theory for the harmonic analysis of these operators, even, in a more general setting that contains Calderón-Zygmund singular integrals of convolution type. In this talk, we present some recent results that extend the Fefferman and Stein theory of oscillating Fourier multipliers to arbitrary Lie groups of polynomial growth. Boundedness properties for pseudo-differential operators and Fourier Integral Operators also are discussed.

References.
[1] Fefferman, C. Inequalities for strongly singular integral operators, Acta Math. 24, 9–36, (1970).
[2] Fefferman, C., Stein, E.Hp spaces of several variables, Acta Math., 129, 137-193, (1972).
[3] Cardona, D., Delgado, J., Ruzhansky, M. Lp-bounds for pseudo-differential operators on graded Lie groups. J. Geom. Anal. Vol. 31, 11603-11647, (2021).